CREATING TEST MECHANISMS FOR SILICON SUBSTRATE BASED (SSB) DEVICES 

FOR USE IN FAR-IR TO MILLIMETER ASTROPHYSICAL SPECTROSCOPY 

 

 

 

 

 

A Thesis 

Presented to the Faculty of the Graduate School 

of Cornell University 

In Partial Fulfillment of the Requirements for the Degree of 

Master of Science in Astronomy and Space Sciences 

 

 

 

 

 

 

by 

Jacquelyn Linevsky 

December 2023 



ii 

 

 

 

 

 

 

 

 

 

 

 

 

© 2023 Jacquelyn Linevsky 

 

 

 

 

 

 

 

 

 



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ABSTRACT 

 

This master’s thesis discusses the technology development, use cases, supporting 

hardware, and developed models for two instruments based on similar technology – the Fabry 

Perot Interferometer (FPI) for use in EoR-Spec instrument and the Virtually Imaged Phase Array 

(VIPA) spectrograph for use in the POEMM (Planetary Origins and Evolution Multispectral 

Monochromator) instrument.  

This paper is divided into three chapters: 

Chapter I, ‘the tip-tilt mechanism’, answers the question of how to design a tip-tilt 

mechanism for a silicon based FPI. By rotating the FPI at variable, measurable angles in either 

direction relative to the incoming beam with one degree rotation increments, while it is cooled in 

a cryostat, we can measure the spectral profile of the FPI. This chapter also provides some technical 

background that is helpful for understanding the POEMM and EoR-Spec instruments discussed in 

chapters two and three. 

Chapter II, ‘POEMM and VIPA’, has two parts. The first walks through the development 

of a model of what the VIPA spectroscopy instrument should detect while searching for 

protoplanetary disks. The next describes the development and laboratory testing of the VIPA 

instrument. POEMM will use a VIPA to spectrally resolve the: [OI] fine-structure line at 63 m, 

HD J=1-0 and J=2-1 rotational lines at 112 and 56 m, H2O rotational lines at 40.7 and 46.5 m 

lines, and H2O ice bands between 35 to 70 microns. POEMM focuses on revealing the evolution 

of the planet-forming mass around a protostar, the changes in distribution and composition of the 



iv 

 

material in protoplanetary disks over time, gaseous matter dissipation via winds or outflows, and 

composition of planetesimals that shape terrestrial and gas-giant cores. 

Chapter III, ‘EoR-Spec’, answers the question of which components to use to adjust the 

FPI spectroscopy instrument. For the EoR-Spec instrument, the Si-based mirrors/filters will be 

used for the FPI. This FPI will be built with a resolving power of about R~100. The science cases 

for EoR-Spec are line intensity mapping, focusing on the [CII] 158 m line and the [OIII] 88 m 

line that can be used to reveal the processes of reionization and galaxy formation in the early 

Universe. [CII] and [OIII] are prime candidates for this science because they are bright and 

associated with star formation.  The [OIII] line traces gas in HII regions formed by OB stars, while 

the [CII] line arises from nearby neutral gas clouds heated by OB star radiation.  

 

 

 

 

 

 

 

 

 

 



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BIOGRAPHICAL SKETCH 

 

Jacquelyn Linevsky was born in Miami, Florida. She attended Cypress Bay High school 

where she developed a passion for astronomy and space sciences. After this, she earned an 

academic scholarship to attend the University of Florida, where she graduated with Suma Cum 

Laude with her BS in Astrophysics and minors in International Studies and Sustainability Studies 

in 2018. Next, Jacquelyn deferred admission from Cornell’s PhD in Astronomy to work at 

NASA’s Jet Propulsion Lab. There, she worked on the Perseverance rover, the Starshade 

mission, and an exoplanet finding mission. At JPL, Jacquelyn also became interested in the fields 

of business and finance in the sciences.  

Jacquelyn embarked on her Astronomy PhD studies at Cornell University in Fall 2020 

while maintaining her newfound interest in business. This interest led her to complement her 

Astronomy studies by enrolling in the Johnson School MBA program. Jacquelyn's commitment 

to astronomy remained unwavering as she resumed her Astronomy studies in the Summer of 

2023, after graduating from the MBA program. She served as a Teaching Assistant for 

Observational Astronomy in Fall 2023. Beyond academia, she engaged two start-up accelerators 

for her Scivisit company and secured a notable $10,000 in funding for the business. 

Jacquelyn made the decision to leave Cornell’s PhD program with a Master’s to pursue a 

transition into consulting with a job offer from one of the world’s top consulting firms, 

McKinsey.  

 

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vi 

 

ACKNOWLEDGEMENTS 

 

I would like to thank Dr. Gordon Stacey for being my advisor, my advocate, and for 

supporting me in my various endeavors, both astronomy research and otherwise, through the years. 

He has been a knowledgeable teacher, expert, mentor in the research realm, and has supported my 

career endeavors.  Dr. Nikole Lewis has been incredibly organized and has helped to keep me on 

track to meet my academic goals. I am grateful for her support in both my academic and 

professional journey. Dr. Terry Herter is a great scientist and teacher, and I am thankful to have 

his support as a member of my committee.  

I also appreciate Dr. Thomas Nikola for advising me on my research with gears and for 

taking the time and patience to help me understand complex ideas.  

I always looked forward to speaking with Monica Carpenter. She has always lent an ear, 

provided me with unwavering encouragement, and helped me to navigate my academic journey 

within Cornell.  

I would also like to extend my thanks to everyone who has been part of my lab journey – 

from past graduate students and current graduate students to engineers and professors. A special 

thank you to Bugao Zou, Ellen Lee, and Rodrigo Freundt. Their collective advice has greatly 

helped me with my project.  

I would also like to thank my family, Leslie Linevsky, Richard Linevsky, Raquel Linevsky, 

and Jesse Linevsky for their enthusiasm, support, and encouragement to achieve great things and 

for their collective advice and support along my Cornell educational path.  

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vii 

 

TABLE OF CONTENTS 

 
BIOGRAPHICAL SKETCH ......................................................................................................... iv 

ACKNOWLEDGEMENTS ............................................................................................................ v 

TABLE OF CONTENTS ............................................................................................................... vi 

CHAPTER I THE TIP-TILT MECHANISM ................................................................................. 1 

Introduction ................................................................................................................................. 1 

Background - How does an FPI work? ....................................................................................... 3 

Background - Silicon FPI ............................................................................................................ 5 

Tip-Tilt Mechanism - Why do we need it? ................................................................................. 7 

Tip-Tilt Mechanism - Test method and parameters .................................................................... 8 

Designing the Tip-Tilt mechanism .............................................................................................. 8 

Challenges and discussion ......................................................................................................... 10 

CHAPTER II POEMM (PLANETARY ORIGINS AND EVOLUTION MULTISPECTRAL 

MONOCHROMATOR) AND VIPA (VIRTUALLY IMAGED PHASE ARRAY) ................... 13 

Introduction ............................................................................................................................... 13 

Science background – protoplanetary disks .............................................................................. 15 

POEMM science instrument ..................................................................................................... 15 

POEMM’s study of protoplanetary disks .................................................................................. 16 

VIPA background ...................................................................................................................... 16 

Similarities and differences between the VIPA and FPI ........................................................... 17 

Development of an interactive velocity curve model for disks ................................................. 19 

Model development ................................................................................................................... 20 

Velocity analysis and Newton's laws ........................................................................................ 24 

Discussion - insights from the model and conclusion ............................................................... 24 

Experimenting with the Cornell VIPA testbed ......................................................................... 26 

VIPA testing and troubleshooting ............................................................................................. 28 

Stray light .................................................................................................................................. 28 

Optical alignment ...................................................................................................................... 30 

Financial and material constraints ............................................................................................. 32 

Summary of challenges encountered......................................................................................... 32 

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viii 

 

CHAPTER III THE EPOCH OF REIONIZATION SPECTROMETER (EOR SPEC) .............. 33 

Introduction ............................................................................................................................... 33 

Science objective: Exploring the birth and growth of galaxies through line intensity mapping.

 ................................................................................................................................................... 34 

EoR-Spec instrument................................................................................................................. 35 

Questions answered and parameters. ........................................................................................ 36 

Stepper motors........................................................................................................................... 37 

Results - fine adjustment screw and worm gear drive: calculations and considerations on 

friction, diameter, and force ...................................................................................................... 40 

Friction coefficient and temperature dependence ..................................................................... 40 

Fine adjustment screw diameter at different temperatures........................................................ 42 

Force on the screw..................................................................................................................... 42 

Discussion ................................................................................................................................. 45 

CHAPTER IV CONCLUSIONS AND FUTURE WORK ........................................................... 45 

For the project ........................................................................................................................... 45 

For me personally ...................................................................................................................... 46 

BIBLIOGRAPHY ......................................................................................................................... 48 

 

 

 

 

 

 

 

 

 

 

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1 
 

CHAPTER I 

THE TIP-TILT MECHANISM 

 

Introduction 

The tip-tilt mechanism’ answers the question of how to design a tip-tilt mechanism for a 

silicon based FPI so that we can measure its spectral profile. We find we can do this by rotating 

the FPI at variable, measurable angles in either direction relative to the incoming beam with one 

degree rotation increments. This chapter also provides some technical background that is helpful 

for understanding the POEMM and EoR-Spec instruments. 

We discuss two types of FPIs (Figure 1). The first is a FPI constructed by coating both 

sides of one thin piece of high purity silicon with a mesh-pattern of gold to make them highly 

reflective, forming a high quality, fixed frequency FPI (FF-FPI).  The second type of FPI is a free-

space FPI (FS-FPI) where there are two thin pieces of high purity silicon, a free space gap, and an 

anti-reflection-coating (ARC). The anti-reflection coat (ARC), for the FS-FPI, is created through 

micromachining of the surface to create air-gaps between pillars of silicon, lowering the refractive 

index in the ARC. The metalized surfaces of the two mirrors of the FS-FPI are then separated from 

one another by a ring to form an air-gap. For both FF-FPI and FS-FPI, gold pattern reflection 

mirrors are photo-lithographically deposited onto silicon wafers creating a thin gold mesh layer 

with inductive and/or capacitive patterns. For this project, we focus on the fixed frequency FPI 

(FF-FPI).  The primary goal of this chapter is to design a turntable mechanism to test the FF-FPI 

and measure its spectral profile.  



2 
 

 

Figure 1: Left image - FF-FPI that we planned to test with the tip-tilt mechanism. We use silicon industry 

technology advancements to deposit the metal photo-lithographically onto the silicon. The metal is gold, 

and the gold mesh pattern is tuned so that it has ~94% reflectance. Right image: FS-FPI with the layers 

labeled. ARC is an anti-reflection coating. We change the wavelength for the FS-FPI changing the space 

between the mirrors.  

 

There are three methods to achieve this goal:  

1. The first approach involves adjusting the distance between mirror surfaces which is only 

possible for the FS- FPI.  

2. The second method is to illuminate the FP with a ~100 micron tunable laser but is not 

practical because we lack access to such a laser.  

3. The third method is using a fixed wavelength laser and tilting the FPI itself to map its 

spectral profile. This is the simplest solution – to tilt the FPI.  

Method 3 requires a tip-tilt mechanism with sufficient resolution and accuracy. We want 

to tip the mirror in one-degree increments with respect to the incoming beam which changes its 

resonant frequency. This tipping (or rotation) enables us to measure the spectral profile of the FPI. 



3 
 

If this mechanical design is successful, it will be used for testing the FPI which could also 

be used in the POEMM (Planetary Origins and Evolution Multispectral Monochrometer) projects. 

This silicon technology has wide-ranging applications in optics and spectroscopy, particularly in 

the mid-infrared to millimeter wavelength range. The development of silicon FPI technology offers 

an improvement over the current use of free-standing metal meshes for far-IR light. By replacing 

free-standing with silicon supported meshes, we can tune the reflector properties to optimize 

performance across a broad range of wavelengths.  

Background - How does an FPI work? 

A typical FPI is a resonance cavity made of two flat, parallel reflecting mirrors. Optical 

waves can be efficiently transmitted through the cavity when they meet the resonant condition 

(Equation 1). Here λ is the transmitted wavelength, and m is the resonant order of the FPI, n is 

refractive index of the material in the cavity, which for silicon is 3.4, d is the distance between the 

mirrors, and θ is the angle of the incoming beam.  

𝑚𝜆

𝑛
= 2 ⅆ 𝑐𝑜𝑠 𝜃 

Equation 1: The FPI resonant condition.  

Light entering the cavity bounces back and forth between the reflective materials and 

makes constructive and destructive interference. The IR electromagnetic radiation wavelengths 

that meet the resonance condition will pass through the mirrors, as shown below in Figure 2. Those 

that do not will be reflected back at the front mirror surface.  



4 
 

One of the most important measures of performance for an FPI is the reflective finesse, F.  

F is defined as the ratio of the distance between resonant peaks at a given wavelength to the full-

width half maximum of a given peak (see Figure 3). 

 

Figure 2: A sketch of a resonance cavity (often referred to as an etalon) made of two flat, parallel reflecting 

mirrors (in blue). The red arrows show the light path of a ray of light. The mirrors are distance d apart. The 

ray comes in at an angle θ and must meet the resonant condition to be passed through the etalon. 

 

If you tilt the FPI, changing θ, the resonant frequency of the cavity changes towards the 

blue as seen in equation 2. For an FF-FPI that consists of one piece of silicon with metallized gold 

surfaces on both sides, the resonant condition is modified by the change of the wavelength of the 

light due to the refractive index of the material in the cavity. The solid silicon FPI we made had a 

silicon thickness of 525 m, and we designed it for use at 100 m wavelength.  

𝛥𝜆 = −𝜆0

𝜃2

2
 

Equation 2: The resonant condition (m λ/n = 2d cos θ) turns into Equation 2 using the small angle 

approximation. 

 

 



5 
 

Background - Silicon FPI 

Free standing metal mesh FPIs have been used in astrophysics for ~50 years. They work 

well. However, they have drawbacks in limited bandwidth of performance, and in absorption 

losses.  

 

 

The goal of this particular silicon FPI is to make an alternative to free-standing meshes 

whose design parameters can be optimized for high performance over broad spectral bandwidths. 

The optical design of a free-standing mesh reflector is limited because it must be able to 

structurally support itself. All conducting elements must therefore be connected as in a window 

screen, so that it has inductive electrical properties, and its reflectivity increases with wavelength. 

Whereas with a silicon substrate, fully capacitive meshes (Figure 4) - consisting of islands of metal 

on a non-conducting substrate, can also be used. A capacitive mesh has reflectivity that decreases 

with wavelength. The mix and match of inductive and capacitive electrical properties can lead to 

uniform finesse over broad ranges [8]. Absorption due to the driving currents that dissipate energy 

in the metal will result in loss in energy: we wish to minimize these losses with an eye on obtaining 

Figure 3: A visual description of finesse. Inter-order 

leakage is power that is transmitted between the peaks. 

 



6 
 

sufficient bandwidth of operation.  This is a challenge because for inductive mesh, the finesse is 

proportional to λ³. This means that when the wavelength increases, the finesse greatly increases, 

resulting in significantly lower transmission due to absorption. The transmission along with the 

finesse make for the primary figures of merit for an FPI. 

Let’s go through an example of the absorption and finesse using our FF-FPI. The 

approximate absorption per pass is ~1%. A good value for F is 50 so that the transmission would 

be ~0.9950 = 60%. The amount of light incident that is transmitted is therefore 60% which is 

generally acceptable. In this calculation, the "50" is an approximation for the number of reflections 

off the mirrors, each time losing 1% of its intensity. While the finesse is not exactly the number of 

bounces, it is related to the resolving power (Equation 3) and wavelength. For another example, if 

F = 100, 0.99100 = 37%, which is not acceptable. 

R = λ / 𝑅𝑃 ≡
𝜆

𝛥𝜆
= 𝐹 ∙ 𝑚;  𝐹 =  

𝜋

(1−𝑅)
√𝑅 

Equation 3: Equation for the resolving power and finesse of a FPI. 

Figure 4: (top) Micrograph of an inductive gold metal grid 

deposited onto silicon. Short wavelengths can be 

transmitted through the inductive mesh whereas long 

wavelengths are reflected.  (bottom) Micrograph of a 

capacitive gold metal mesh deposited onto silicon. Long 

wavelengths can be transmitted through the capacitive 

mesh whereas short wavelengths are reflected.   

 

 

                   

                    

     

     



7 
 

We are working to flatten the finesse over broadbands to make for high efficiency with the 

FS-FPI. Specifically, we want to flatten the finesse over the 210 GHz to 420 GHz frequency of 

EoR-Spec (discussed in Chapter III). We typically want a finesse between 30 and 70. Below 30 

and there is too much inter-order leakage (transmission between the peaks, see Figure 3) and above 

70, there is too much absorption. If successful, the FPI’s capability to resolve spectral features 

should remain the same, whether it is operating at 210 GHz or 420 GHz. In the future, we are 

envisioning superconducting metal meshes so that the Ohmic losses go to nearly zero. 

With the FF SSB FPI we expect a finesse of 50. Operating in 38th order, the expected 

resolving power is 1900. This is the width of the fringe we hope to measure. However, our far-IR 

FTS is limited to a resolving power of 0.125 wavenumbers, or a resolving power of 100/0.125=800 

at 100 m. We decided to make the tip-tilt mechanism since we needed to measure the profile 

better than that which the FTS could deliver. 

Tip-Tilt Mechanism - Why do we need it? 

The device will test the FPI by holding, translating, and tipping it with respect to the 

incoming beam which changes its resonant wavelength, as indicated by Equation 1. To properly 

map out the spectral profile, we need to access wavelengths up to ~2% different than the profile 

center wavelength. Our laser has a center wavelength of 79 m to that this corresponds to a shift 

of ~1.6 m.  Using Equation 2 we get a tilt maximum tilt of 11.5 degrees. To find the minimum 

tilt angle, we use the Nyquist criterion, which states that to accurately sample a signal, you need 

to sample at least twice as frequently as the highest frequency. For our FF-FPI, we have a resolving 

power of 2000, so we need to sample 1/4000 of the wavelength. For 79 m, 79/4000=0.02m. 

From Equation 2, this corresponds to a tilt angle of 1.3 degrees.  



8 
 

Having found our desired measurement range, we decided to rotate FPI with 1 degree 

accuracy to be on the conservative side to secure a good measurement of the FPI spectral profile. 

In the future, we plan to observe spectral lines over a wide field with high resolving power in the 

far infrared (30 m – 200 m wavelength). 

Tip-Tilt Mechanism - Test method and parameters 

The test method is to shine a 79 m laser through the FPI and use the push-pull mechanism 

to insert and withdraw the FPI into and out of the light beam to get the efficiency of the FPI 

(transmission). The entire turntable mechanism will be cooled down inside a cryostat to ~4K.  

There were several parameters regarding size, temperature, material, and rotation of the tip 

tilt mechanism. The test set up parameters had a test Dewar with windows on both sides, which is 

just large enough to fit a FPI. The filter will be cooled in a science configuration to 4 K to freeze 

out impurity carriers and maximize the filter transmission in the far-IR.  Therefore, the filter and 

the turntable mechanism will be cooled in a liquid helium cryostat. 

Designing the Tip-Tilt mechanism 

Figures 5 and 6 depict the wavelength change that corresponds to various degrees of 

turntable shift with different wavelengths of light that we plan to observe and measure. The x-axis 

is the turntable rotation angle in degrees, and the y-axis is in microns. Applying Equation 2, Figure 

5 shows the shift in wavelength with tilt at our nominal wavelength of 79 m. Figure 6 is similar 

but shows the shift for several ion and molecule lines of interest. Using a gear ratio to move the 

tip tilt mechanism is the best way to ensure an accurate and measurable angle movement. The goal 

for the turntable mechanism is to have an accuracy of 1 degree movement. Using Equation 2 and 



9 
 

the 79 m line as an example, we can calculate that one degree of shift from normal incidence 

corresponds to a wavelength shift of -0.012 m (blueshifted) [2], [6].   

  

  

Table 1 below lists the characteristics of the gears we chose for the mechanism, which are 

available from McMaster-Carr.  The larger gear has an outer diameter of 45 mm and has 45 teeth 

whereas the smaller gear has an outer diameter of 15 mm and has 15 teeth. This makes for a gear 

ratio of 3:1 (45/15=3) which means that it takes 3 full rotations of the small gear to move the big 

Figure 6: The X axis is degrees of 

turntable tilt and the Y axis is the 

change in wavelength in m. The 

different colors are what we might 

see with different wavelengths of 

interest including [OIII] 88 m, [CII] 

158 m, [OI] 63 m, HD (1-0) 112 

m, (2-1) 56 m, H2O 46 m and 41 

m.  

Figure 5: The X axis is degrees of 

turntable tilt and the Y axis is the 

change in wavelength in m. The line 

center is at 79 m.  



10 
 

gear 1 full rotation. The big gear is the tip-tilt angle change. This means that to meet the goal of 

one degree of rotation of the tip-tilt mechanism, the small gear will need to rotate 3 degrees. 

Table 1: Gear Characteristics  

Outer 

Diameter 

Number 

of Teeth 

Part 

Number 

Price 

45mm 45 2515N337 $42.33 

15mm 15 2515N333 $21.96 

 

 

The tip tilt mechanism was designed using SolidWorks 2019. Figure 7 depicts a 3D 

modeled Solid Works design of the tip-tilt mechanism. The different components of the image are 

numbered and called out in the figure caption.  

Challenges and discussion 

Designing the tip-tilt mechanism for the project posed several challenges, including those 

related to temperature, size, limited access to the FPI, and vacuum conditions. Variations in 

temperature can lead to material warpage, shrinkage, expansion, and outgassing, all of which can 

impact the mechanism's performance. In addition, silicon, which exhibits high electromagnetic 

wave absorption at room temperature, requires cooling to minimize absorption effects. Other 

challenges included taking precise measurements, and lack of accessibility to the mechanism.  

In the end, we didn’t complete the construction of the tip-tilt mechanism because at the 

time, we were unable to acquire a suitable laser with which we could make the profile 

Table 1: Gear characteristics for 45 degree bevel gears from McMaster-Carr. The table includes 

outer diameter, number of teeth on gear, the part number and the price.  



11 
 

measurements.  As a fallback, we made cold measurements with our FTS and corrected from the 

insufficient resolving power of the FTS by convolving the expected spectrum with the spectral 

profile of the FTS, which was then compared with the measurements.   

Graduate student Bugao Zou used a microwave simulation program to model the 

performance of our FF-FPI including the reflectivity as a function of the wavelength (Figure 8).  

The model predicts RP ~ 2000, but the RP of the FTS is smaller, so he convolved the predicted 

spectrum with the Happ-Genzel spectroscopic window for the FTS to show that we are measuring 

what is predicted. The FTS measurements (orange) are in excellent agreement with the convolution 

of the FTS spectral profile (black) from Zou’s calculations.  

 

Figure 7:  Final design of the tip-tilt mechanism using SolidWorks. The different components of the image 

are numbered. #1 and #2 are the bevel gears. # 3 is the push-pull and rotation shaft that goes from inside 

the Dewar to room temperature. This shaft is used to pull, push, and tip the entire mechanism. #4 is the 

Dewar window. #5 is the work surface of the Dewar. #6 is the slide rail. #7 is the holding device for the 

FPI that gets tipped and translated. #8 is an optional gear box to refine rotation angles when required.  



12 
 

It is necessary to confirm these predictions, and we will do this by either using our turntable 

mechanism design within the cryostat testbed and a fixed frequency far-IR laser or purchasing a 

tunable far-IR laser.  The tunable laser is an excellent option in that it could then be used for testing 

a wide variety of FPI for POEMM or other programs.  

 

 

Figure 8: The far-infrared Fourier-transform spectrometer (FTS) measurements (orange lines) and the 

computer simulation for a silicon-cavity-based Fabry-Pérot interferometer (black lines). The silicon 

substrate has a set of inductive gold grids on its outer surface. The spikes in the spectrum are due to water 

vapor lines that do not divide out well in the transmittance spectrum. This Figure is from ref. [8]. 

 

 

 

 

 

 



13 
 

CHAPTER II 

POEMM (PLANETARY ORIGINS AND EVOLUTION MULTISPECTRAL 

MONOCHROMATOR) AND VIPA (VIRTUALLY IMAGED PHASE ARRAY) 

 

Introduction  

The research conducted in Chapter II of this paper focuses on the proposed POEMM 

mission and VIPA instrument. The VIPA technology shares similarities with the FPI (Fabry-Perot 

Interferometer) discussed in Chapter I of this paper, establishing a strong foundation for this work. 

This chapter starts with a broad science background which includes the science goals, an 

introduction to the POEMM mission, the science instrument, and the VIPA (Virtually Image 

Phased Array) spectrograph. Then we delve into my specific contributions.  

The two primary areas of contributions include:  

1. The development of an interactive velocity curve model for protoplanetary disks  

The study of protoplanetary disks in astrophysics is vital to understanding planet formation. 

This section helps in answering the questions of what will the VIPA science instrument ‘see’ when 

observing protoplanetary disks. Here, we describe simplified model that interactively shows how 

the velocity curve for rings in orbit about a star translate into the spectrum based on the mass of 

central star as a function of the inner and outer ring radius, the inclination angle of the ring, the 

gas temperature and mass of composition of the disk. The VIPA should be capable of detecting 

differences in the Doppler shifted motion of material in protoplanetary disks to track these 

parameters.  



14 
 

The VIPA spectrometer is still under development in conjunction with theoretical models 

that are compared with the VIPA experimental results. We have models of expected VIPA 

performance and collaborators on POEMM have models of line emission from protoplanetary disk, 

so we know what to expect. However, I built my own toy model of a protoplanetary disk by 

applying applications of Newton’s laws to orbits with an addition term to include thermal line 

widths.  The model described below is at a basic level and further work needs to be completed to 

include the line emission from various species expected in protoplanetary disks. For example, a 

more complete model needs to include the thermal balance, line excitation mechanisms, and 

radiative transfer to predict the expected line flux from abundant species such as water, HD, and 

oxygen. The further development of the model is out of the scope of this master’s thesis paper.  

2. Experimenting with the VIPA testbed 

Here we discuss the requirements for testing the VIPA:  how to do the measurements, 

including what we tried – sending a continuum radiation through the cold VIPA, and our next steps 

which included using a 115 micron far-IR laser for testing. This chapter describes the series of 

attempts to trace out the spectral profile of a VIPA using the UCB (University of California 

Berkley) FPI.  

The POEMM mission is designed to enable a better understand the evolution of the total 

planet-forming mass around a protostar, the changes in distribution and composition of the 

protoplanetary disk as the disk evolves in time, the dissipation of gaseous matter through winds or 

outflows, and the composition of planetesimals that form terrestrial planets and gas-giant cores.  

POEMM provides wavelength (spectral-line) coverage and sensitivities not available with ground-

based facilities. 



15 
 

Science background – protoplanetary disks 

Protostars are created in giant molecular cloud condensations of gas and dust accumulating 

around the protostar. Due to the conservation of angular momentum, the collapse process results 

in the cloud flattening into a disk perpendicular to its axis of rotation. This disk-shaped cloud of 

gas, dust, and debris eventually can turn into planets and is known as a protoplanetary disk [7]. 

Measuring the evolution of the total planet-forming mass around a protostar is critical to an 

understanding of planet formation. 

Astronomers have identified many protoplanetary disks, including some with gaps that 

might reveal the presence of a planet being formed. The structure of these disks provides clues to 

where planets form, how they form, their chemical and physical composition, the size and shapes 

of the orbits, and how orbits may evolve after formation.  Scientists use models to understand how 

the structure and chemical processes involving gases and solid-state materials (such as ice) change 

over the evolution of planetary systems. The structure and time evolution of the gases and ices are 

important to model to help in our understanding of the final populations of planetary systems. The 

Earth formed hot and dry. Therefore, another aspect of study is how water is transported to 

terrestrial planets, which is a crucial element of the formation of Earth-like planets and their 

habitability [7]. 

POEMM science instrument 

The POEMM mission is currently in its initial stages of development at Cornell. It is a 

proposed NASA Pioneers mission in collaboration with NASA Goddard and is based on a balloon 

platform. The VIPA is the enabling technology for the POEMM mission. It use is also called for 

in a NASA Probe mission proposal, called the Far-Infrared Spectroscopic Survey Probe (FIRSST).   



16 
 

The VIPA is a cryogenic spectrometer designed to observe far-infrared wavelengths that 

are not visible from terrestrial locations. POEMM is proposed to observe ionic and molecular lines: 

[OI] 63 m, HD 112 m and 56 m, H2O 40.7 m and 46.5 m, and H2O ice bands between 35 

to 70 microns. 

POEMM’s study of protoplanetary disks 

The VIPA spectrometers, essentially tilted Fabry-Perot Interferometers, are designed to 

observe lines at wavelengths ranging from 50 to approximately 300 m in the far-infrared. These 

far-infrared lines are important because they serve as powerful tracers of the building blocks of 

planetary systems and can only be observed from high-altitude balloon or space-based telescopes 

because the atmosphere absorbs these wavelengths at ground level. Currently, there is no 

observatory providing access to this spectral range.  

Here we plan to reveal the mass of important gaseous species (H2O, HD, and [OI]) as a 

function of radial distance from the central star by velocity resolving the line emission.  The 

velocity information combined with Newton’s orbital laws reveal the locations of the emitting gas 

within the disk at AU scales, providing valuable insights into the mass distribution and chemical 

properties of the protoplanetary disk. The lines we chose are optically thin and collisionally excited 

so that the line emission traces the mass of the emitted species in a straight-forward manner. 

VIPA background 

POEMM's science instrument incorporates three VIPA spectrometers. As discussed in 

Chapter 1, the VIPA, essentially a tilted Fabry-Perot etalon, plays a crucial role in achieving high-

resolution spectroscopy. Each VIPA is designed with a resolving power 𝛥𝑣 ~ 3 km/sec.  



17 
 

At wavelengths longer than about 70 um, cryogenic ultra-pure silicon is transmissive – 

especially when cooled to cryogenic temperatures, thus the VIPAs are based on solid silicon 

resonant cavities, like those described in Part I. The choice of silicon as the material for the VIPA 

resonant cavities utilizes its unique properties and takes advantage of silicon lithography and 

micromachining techniques, enabling high-performance spectroscopic devices for the far-infrared 

part of the spectrum. 

 

Similarities and differences between the VIPA and FPI 

At a first glance, the VIPA shares similarities with the Fabry-Perot Interferometer (FPI) 

discussed in Chapter I in its use of two highly reflective, metalized mirrors held in a plane-parallel 

configuration to form a resonant cavity (Figure 9). However, there are significant distinctions that 

set the VIPA apart from the FPI. Both systems offer exceptional resolving power (RP > 105) while 

maintaining a compact design [1], but the VIPA spectrally multiplexes.  

 

 

Figure 9: The left image shows light path through the VIPA device. First, a cylindrical mirror forms a line 

focus that is sent into the tilted VIPA through an entrance slit. The tilt is such that the focus (at the 90% 

reflective back mirror) reflects back to the 100% reflective front mirror from which it then begins walking 

up the cavity.  The operations of the VIPA can be thought of as producing images at larger and larger phase 

delays as the light bounces down the cavity. These reflections in the etalon produce a series of virtual 

sources, each shifted up and to the left. The diverging beams from these virtual images produce a dispersed 

spectrum. The righthand image shows Cornell’s far-IR VIPA in its optical bench configuration before 

cryogenic tests.  



18 
 

While the FPI is typically positioned within the pupil of an optical system, the VIPA uses 

a cylindrical mirror to illuminate the VIPA in a line focus along an edge slit. This design and the 

non-identical mirrors with a slight tilt in the image plane direction, enables the passage of light 

down the resonant cavity. By doing so, the VIPA provides continuous resonant paths for a broad 

range of frequencies, resulting in an instantaneous, broad spectrum without the need for spectral 

scanning.  

The VIPA’s ability to measure a complete spectrum simultaneously makes it convenient, 

efficient, and more versatile than traditional spectrometers. An additional advantage is that the 

silicon substrate-based VIPA has no moving parts and is much more compact than a free-space 

FPI due to the high index of refraction of silicon.  

It is also practical for space missions. Current choices for space missions include grating 

spectrometers (GS), FTS instruments, FPI and now, VIPA spectrometers. The GS and FTS 

spectrometers would need to be quite large at far-IR wavelengths to deliver resolving powers ~ 3 

km/s.  In contrast, the multi-pass FPI and VIPA are quite compact. The VIPA has a large advantage 

over the FPI in that the FPI requires spectral scanning, but the VIPA doesn't. It spectrally 

multiplexes and can provide a detailed spectrum with up to approximately 33 spectral resolution 

elements which opens new possibilities for scientific research and applications. For a 33-element 

spectrum, the VIPA is 33 times faster and therefore effectively √33 times more sensitive than FPI, 

since the sensitivity is linked to the signal-to-noise ratio by (S/N = √𝑡). The VIPA can observe a 

wide range of frequencies – and, as mentioned earlier, we plan for between 40 and 300 microns in 

the far-infrared. It can also easily achieve <3 km/sec resolving power and therefore can resolve the 

Keplerian rotational motions of protoplanetary disks. 

 



19 
 

Development of an interactive velocity curve model for disks  

To visualize how line velocities translate into orbital radii within a protoplanetary disk, I 

created a simple prototype model of how the VIPA velocity curves might look like as a function 

of the intensity of material in a protoplanetary disk. 

One way of studying protoplanetary disks involves using the Doppler shift - detecting 

changes in light wavelengths caused by the movement of gas within the disk using radial velocity 

methods.  The non-relativistic Doppler shift equation is given below (Equation 4). Here Δλ 

represents the change in wavelength due to the Doppler shift, λ represents the rest wavelength of 

the spectral line being observed, v represents the velocity of the object causing the Doppler shift, 

and c is the speed of light. 

Δλ/λ = v/c 

Equation 4: The non-relativistic Doppler shift formula. This is used in the protoplanetary disk model to 

see the variations in line-of-sight velocity as material orbits the central star. 

Implemented in Excel, the model helps us understand how the VIPA instrument sees these 

disks and helps to predict what the data will look like when observing a protoplanetary disk. Inputs 

include the mass of the central star line intensity, the tilt of the disk relative to the line of sight of 

the observer and assume Keplerian motions of the gas. The model uses three rings of material 

around the star, each with its orbital radius and emissivity as outlined below, to give insight into 

how gaps in the disk change the velocity profile. 

By considering the variations in material velocity as it orbits the central star, the model 

reveals how these movements result in slightly different wavelengths that can be detected and 



20 
 

resolved by the VIPA. By analyzing the changes in wavelength and corresponding intensities of 

spectral lines emitted by the gas or objects in protoplanetary disks, one can study the dynamics 

(which reflect the orbital radius) and mass of the protoplanetary system. 

Model development 

The expected line profile for our model of a single ring of emitting gas orbiting a protostar 

is shown in Figure 10.  The yellow boxes in the accompanying table indicate changeable inputs to 

the model including: mass of the central star, disk tilt angle of with respect to the line of sign to 

the observer, line intensity of the disk, velocity of the disk (as a function of radius from the central 

star), width of the disk, the intrinsic line width (thermal) of the emitting species in the disk, and a 

composite velocity curve to combine multiple protoplanetary rings around a central star. The plot 

shows the line profile for gas at 1 AU from the star based on the parameters indicated in yellow. 

 

 

 

 

 

 



21 
 

 

 

Figure 10: On the top, we see the model predicted two-horned profile of the change in velocity of the 

material moving around the star. On the x axis is velocity (both towards and away from the observer), on 

the y axis is intensity. On the bottom, we see the yellow highlighted inputs which allow for an interactive 

plot. First, the mass of star, which in this case, is set to a sun-like star, the inner and outer velocity of the 

material in the ring, the angle tilt of the ring relative to an observer, the line intensity as taken on an arbitrary 

scale, the temperature of the material in the ring, and the atomic mass of the emitting species used in 

calculating its thermal line-wide in the ring. On the tip right, we have the Keplerian formula.  

 

 

 



22 
 

 

Figure 11:  Three protoplanetary disks superimposed on top of each other. The inputs to create these disks 

are shown in Table 2. The x-axis is the line-of-sight Doppler component of the velocity, and the y axis is 

arbitrary intensity.  

 

Figure 11 shows a case with three planet forming rings with different characteristics. Each 

color corresponds to a different ring orbiting the same central star, all superimposed on top of each 

other.  

In Table 2 below, the yellow highlighted boxes are inputs used for Figure 12. In this 

example of the model output, all three protoplanetary disks are orbiting around a solar-mass star. 

The inner ring velocity and outer ring velocities are all different, with the orange being closest to 

the star, followed by blue and finally gray. The change in speeds is reflective of the Keplerian 

behavior of the disk. The magnitude corresponds to the emissivity of the orbiting material in a 

simple disk and the temperature is the average temperature of the material in the disk. In this 

example, for simplicity and clarity the temperature of orbiting material is set at 300K, for all three 

rings. Finally, the thermal line width computed as   
1

2
𝑚(𝑣𝑡ℎ𝑒𝑟𝑚𝑎𝑙)

2 =
3

2
𝑘𝑇 is 2.7 km/sec for H 

atoms.  The only difference between the three rings is the orbital radius. 



23 
 

 

 

 

 

Below, in Figure 12, we combined the three superimposed material rings from Figure 11 

into a composite graph to simulate more realistically what we might see in an actual protoplanetary 

disk spectrum with the VIPA.  In general, the VIPA will not spatially resolve the disk and the 

observed spectrum will be integrated over the rings at a given velocity.  

 

Table 2: The yellow boxes indicate the input values for 3 protoplanetary disks around the same star. 

The ‘Orange’, ‘Blue, and ‘Gray’ correspond to a different disk around the same central star, and it 

corresponds to its colored curve.   

Table 2: Input values for disk model 



24 
 

 

Figure 12: Composite image combining three disks into one graphical image. The x axis is the Doppler 

velocity of the material as orbits the protostar, the y axis is the relative intensity of that material.  

 

Velocity analysis and Newton's laws 

Based on Newton's laws, equating centripetal acceleration to gravitational acceleration, we 

have: 
1

2
𝑚𝑣2 = 𝐺

𝑀𝑚

𝑟2  where m is the mass of the object, M is the mass of the star, r is the radius 

from the star, and v is the velocity of the object moving around the star. Solving this equation for 

v results in 𝑣 =
𝐺𝑀

𝑟2 . This shows us that the differences in velocity as a function of position around 

a star can be mapped out. The velocity is linked to the Doppler shifted wavelength. By analyzing 

the velocity information and applying Newton's orbital laws, the VIPA plays a crucial role in 

determining the precise location of gas within a protoplanetary disk, down to astronomical units 

(AU) or sub-AU scales. For example, at r = 1AU and M* = M⊙ yields a velocity of 30 km/s, easily 

discernable within the VIPA spectrum. 

Discussion - insights from the model and conclusion 

This model shows that the VIPA detector can be used for investigating the dynamics and 

composition of protoplanetary disks, enriching our understanding of the processes involved in 

planet formation and the evolution of young stellar systems. However, our model uses some 



25 
 

simplifications for both the protoplanetary disk as well as the instrument that we plan to improve 

in future studies. For example, we assume that the disk is circular, the material in each segment of 

the disk is distributed evenly, and that the central object is a singular star. While protoplanetary 

disks can have irregular shapes, most observed disks show elliptical shapes so modeling a circular 

orbit is of interest. While a central binary star system can influence the inner edge as well as the 

width of a protoplanetary disk, we have concentrated on a single star central object for our 

simulations. We also do not consider the luminosity of the central star (although it is extremely 

unlikely to be a strong emitter in [OI], H2O or HD), only that of the disk. Additionally, the line 

intensity scale is arbitrary and is related to the amount of mass in the system. This is not an 

astrophysically calculated intensity which would be a function of the abundance and excitation of 

the emitting species. We have also not discussed detection limits. Modeling that compares the 

actual VIPA resolution and sensitivity detection limits to the disk emission curves predicted by the 

science team has already been started by Thomas Nikola. We plan to address these topics in a 

future investigation.  

We will need to physically test this, or the more sophisticated models developed by the 

science team, to see if they are comparable to what we will experimentally see.  Our model can 

help to understand the specific characteristics of multiple ring systems around a central star and to 

break them down into individual ring systems. The VIPA should enhance our knowledge of 

protoplanetary disk evolution, shedding light on the processes of planet formation and the 

distribution of material within these systems.    

 

 

 



26 
 

Experimenting with the Cornell VIPA testbed   

The Cornell team has created a first-generation silicon VIPA at Cornell using a 1 cm 

(thick)× 3 cm (wide) × 5 cm (long) thick piece of high purity silicon centered at the 112 μm HD 

line.  We also created a VIPA test bed based on heritage equipment from our lab (Figure 13). 

 

 

Figure 13: This is a schematic of the VIPA test bed. The system starts with the chopper (the black box). 

The chopped light enters from the left-hand side. A collimating mirror sends the light through a very high 

resolving power room temperature FPI.  The beam then enters the VIPA cryostat where it is focused on the 

VIPA slit by a cylindrical mirror. The VIPA delivers a 2-d collimated beam that then exits the VIPA cryostat 

and is focused within the 2 K detector UC Berkeley cryostat on a Sb:Ga photodetector where the radiation 

is detected. (Note that in this schematic, the mirrors are illustrated as lenses for simplicity of showing a 

layout.)  Source: GJ Stacey personal communication 

 



27 
 

To make the VIPA work as a spectrometer, it is tilted at an angle to the incoming light so 

that the light beam ‘walks’ up the device as it bounces between the reflective plates. Each 

wavelength finds its own path based on the resonance condition within the cavity: 

mλ/2 = nD×cos(θ), where m is the order of the resonance, n is the refractive index of the medium 

between the mirrors, and θ is the angle of resonance at each wavelength.  

The VIPA sits inside of an optical test-Dewar that has been modified to fit an optical bench 

(Figure 14). The entrance to the system accepts a 1-inch diameter collimated beamed which is then 

focused by a cylindrical mirror onto the VIPA entrance slit. [8]  

 

Figure 14: Hardware design in lab of the VIPA test stand with the aluminum baffles 



28 
 

 

The detector system is a heritage far-IR spectrometer (reference PhD Thesis J.B. Lugten 

1986) that uses a high-resolution FPI. The resonant orders of the FPI are selected by fixed-

wavelength filters. [1]  

VIPA testing and troubleshooting  

Testing the VIPA in the hybrid setup we have is quite challenging. Some of the challenges 

included: 1. Stray light interference; 2. Precise optical alignment; 3. Financial/material constraints; 

and 4. Lack of a suitable laser for continuous alignment. Each of these challenges is described in 

more detail below. Several attempts were made to collect the first measurement from the VIPA 

using the test set up described above, but none of them yielded useful results. 

Stray light  

The first measurements yield detectable far-IR light through the VIPA cryostat, but this 

was determined not to be light that had gone through the system. One hypothesis proposed by the 

team was that the stray light observed might have resulted from residual light reflecting off the 

aluminum surface. To investigate this hypothesis, aluminum baffles were constructed to prevent 

stray light from reaching the detector. The baffles were designed, measured, and installed, with 

surfaces lined with thin sheets of cardboard to absorb far-IR radiation. Aluminum both supported 

and cooled the cardboard. This hypothesis was subsequently confirmed, as the implementation of 

cardboard and aluminum baffles did effectively mitigate the stray light interference caused by 

reflective light. 

During the testing phase with the cardboard inserts, a separate, minor, issue arose 

concerning the vacuum levels. Despite conducting multiple leak tests, the desired vacuum 

conditions were not low enough. The likely explanation as out gassing of water vapor trapped in 



29 
 

cardboard. The cardboard and aluminum baffles are shown in Figure 15. This was verified as the 

issue went away over time and eventually, the required high vacuum level was reached.  

 

 

Figure 15: Cardboard was installed to eliminate stray light paths and to make an absorptive surface. 

 

After successfully addressing the reflective light issue with the cardboard inserts, as shown 

in Figure 15 the research team encountered persistent difficulties in obtaining a measurement. As 

a result, the focus shifted towards investigating the alignment of the optical components as a 

probable cause.  

 



30 
 

Optical alignment  

The main challenge is that the VIPA does not transmit optical light, making laser alignment 

challenging without an IR laser. We still did partial alignments using the visible light (HeNe) laser, 

as shown in Figure 16, to ensure that the rest of the system was aligned. The emitting optics, VIPA 

Dewar, and the detector Dewar, all need to have the principal ray of the entire system translate 

through the entire system to high accuracy. The entrance beam should hit the slit within +/- 0.2mm. 

It is also important to have the correct angle of injection so that the light walks through the device. 

(Figure 17). In the end we expect that we were not ever able to get a signal through the system 

because the optical alignment was extremely challenging, complicated by the fact that the VIPA 

parameters were not well understood during the time of testing, so the VIPA entrance angle was 

non-optimal.  

 To simplify the optical path, in our second attempt at measurement we eliminated the warm 

high-res FPI from the optical path (Figure 13), focusing on just the RP = 20,000 FPI (the UCB 

FPI) to trace out the profile of the VIPA (also about RP = 20,000). The co-alignment of the UCB 

and VIPA f-cones is critical to achieve these resolving powers in both high-resolution devices. 

This is a tip/tilt adjustment which is equivalent to aligning the chief ray. Also, another challenge 

is that there is only one pixel within the UCB FPI detector, so we also needed to have the focal 

planes that exit the VIPA Dewar aligned in x and y. Additionally, the foci of the two optical 

systems need to match (in the z direction). The optical systems were mounted on independent 

benches making their co-alignment very challenging. Finally, another challenge is the thickness of 

the silicon material for the VIPA is known to a fraction of a mm, but not to the micron level. The 

thickness determines the resonant angle for the system, as shown in Equation 1, so that even if all 



31 
 

else were aligned, it was conceivable that the light was coming out of the VIPA at an angle that 

was essentially unknown.  

 

Figure 16: (left) Optical set-up for the VIPA testing. The VIPA is in the blue Dewar.  In the foreground is 

a collimated light and chopper system that injects light into the VIPA cryostat where it is collimated by the 

cylindrical lens.  The exit from the VIPA dewar is to the left where the light is focused and sent into the 

UCB FPI for detections. (right) Optical laser alignment with a visible light laser. This optical laser 

alignment helped to ensure that all components, besides the VIPA, were aligned. The visible light laser 

does not do an end-to-end alignment, but the (later) use of a quantum cascade laser from Long Wave 

Photonics does.  

 

 



32 
 

 

 

 

 

 

 

 
 

Figure 17: Schematic operating principle of a VIPA.  Light enters the VIPA along a line focus from the 

left is dispersed within the VIPA, then exits the VIPA to the right to be focused on a detector array. 

Source: GJ Stacey personal communication  
 

 

Financial and material constraints  

Each test conducted with this setup necessitated the consumption of a considerable amount 

of liquid helium, typically exceeding 100 liters. This posed both financial constraints and 

availability issues, as liquid helium is an expensive and often scarce resource.  

Summary of challenges encountered.  

In summary, the research process involving the VIPA test bed at Cornell University 

encountered significant challenges, including reflective stray light interference, optical alignment 

issues, cooling-induced shrinkage, and financial/material constraints. Additionally, the lack of a 

suitable laser for continuous alignment proved to be a major obstacle in this effort.  

To overcome these challenges and perform a comprehensive end-to-end optical alignment, 

we searched for and found a quantum cascade laser operating at 2.7 THz (115 m) in the far 

infrared range to simplify the system. Unfortunately, neither Cornell's campus nor the NASA 

Goddard site had such a laser, leading to a three-month delay in the operation. In May 2023, a 

           

       
                       

                      

         
     

            
    



33 
 

suitable quantum cascade laser was obtained from Long Wave Photonics (Sunnyvale, CA) and is 

currently being tested (with great success) in the lab by graduate student Bugao Zou and Dr. 

Thomas Nikola. The QCL emits a laser line that can be collimated and sent into the VIPA optics 

while warm where it was detectable with a room temperature detector. The biggest challenge to 

the new system was understanding the output of the QCL. 

 

CHAPTER III 

THE EPOCH OF REIONIZATION SPECTROMETER (EOR SPEC) 

 

Introduction 

We are building an instrument, called EoR-spec, for the Fred Young Submillimeter 

Telescope (FYST) telescope which will be sited at 5600 m elevator near the peak of Cerro 

Chajnantor in northern Chile. The properties of FYST ensure very high mapping speeds in the 

submillimeter telluric windows: it is located at a very high and dry site, it has very low 

emissivity, and it has an exceptionally wide field of view, up to 8 degrees at 3 mm wavelength. 

EoR-Spec is one (or two) of the 7 instrument modules that will make up the PrimeCam receiver 

for FYST that is being developed at Cornell University.  

The science objective of EoR-Spec is to detect the evolution of the structure and formation 

of galaxies in the Universe from the epoch of reionization through to the epoch of peak star 

formation in the Universe. Specifically, we are looking at the redshift range from z ~ 8 to 3.5 which 

covers the time period from end of reionization to the beginning of the cosmic noon - the period 

when the rate of star formation per unit comoving volume in the history of the Universe peaked. 



34 
 

EoR-Spec is based on a submillimeter FPI with a clear aperture of 14 cm. Our goal here is 

to find the appropriate gears, screws, and motors that should be used for the EoR-Spec tip-tilt 

parallelism adjust mechanism for its FPI mirrors. A major concern is that the cryogenic motors 

have enough torque to drive the gear chains at cryogenic temperatures. 

In this chapter, mathematical analysis and derivation checks of the gear formula are 

conducted to develop an Excel model describing the friction, force, and torques of the fine 

adjustment screw and worm gear drive. This is an expansion of the work done by Thomas Nikola 

and by former student Ellen Lee. 

Science objective: Exploring the birth and growth of galaxies through line intensity mapping.  

 13.8 billion years ago at the start of the Universe, the hot Big Bang expanded from an 

extreme temperature and density plasma that cooled and became less dense as the Universe 

expanded. The Epoch of recombination occurred when T < 4000 K, which was cool enough for 

electrons to combine with protons to form neutral hydrogen atoms, releasing photons which we 

detect as the CMB. Next, after recombination, normal matter was fully decoupled from radiation 

so that it then could be gravitationally accreted onto the underlying dark matter structures that had 

already formed. The distribution of dark matter structures over cosmic time is closely tied to 

fundamental cosmological questions, including the number and mass of neutrinos in the Universe, 

the equation of state of dark matter, and considerations related to inflation.  

The Epoch of Reionization spectrometer is being developed to explore the evolution of 

galaxies from near the end of the epoch of reionization to near the start of cosmic noon. We want 

to better understand the intensity and spatial distribution of these galaxies to understand early 

formation theory [9]. Observations of [CII] line emission from local and high-redshift galaxies 

show that it is one of the best tracers of the properties of star formation because [CII] measures the 



35 
 

intensity of far ultraviolet radiation fields from OB stars thereby tracing star formation, albeit in 

an indirect manner. The [CII] fine-structure line transition has a rest wavelength of 158 μm (1901 

GHz frequency) so that EoR-Spec must address frequencies from 210 to 420 GHz corresponding 

to z ~ 8 to 3.5 [9]. This [CII] line intensity mapping survey is the primary goal, but other lines such 

as [OIII] 88 m and low and mid-J CO rotational lines will also be traced at higher, and lower 

redshifts respectively. [OIII] traces high ionization sources (O stars) and the CO lines trace the 

neutral gas that fuels star formation. 

EoR-Spec instrument 

 The EoR-Spec instrument was designed for FYST which is well suited for wide-field 

intensity mapping experiments, e.g., CMB and line intensity mapping. The science requirement is 

that the resolving power be about ~100. We will be making a map of 2∘ × 4∘ regions which are 

big enough to sample for the structure of both star forming regions and dark matter in the cosmic 

web. The beam size of EoR-Spec on FYST is about 45” which corresponds to about 0.3 Mpc at 

these redshifts - well suited to resolve the peaks of star formation activity.  

The EoR-Spec instrument utilizes a free space silicon substrate-based scanning Fabry-

Perot interferometer (FPI), like the kind discussed in part 1 of this paper.  The FPI is in an optical 

pupil of the system and will illuminate arrays of about 6000 beams to maximize the mapping speed.  

FPIs are well suited for scanning and mapping larger areas of the sky, whereas by its nature, a 

VIPA is the instrument of choice for point sources. An FPI is the choice for EoR-Spec since the 

science goal of this instrument is to map large scale structures on the sky.  



36 
 

The Prime-Cam cryostat (Figure 18) provides a common 4 K flange to which all instrument 

modules are being mounted. The FPI and its components are cooled to 4K and below to reduce 

thermal radiation thereby minimizing noise and enhancing signal detection.   

Figure 18: The Prime-Cam cryostat houses seven instrument modules. Indicated are potential locations 

for the two EoR-Spec modules. [9]  

 

 

Questions answered and parameters. 

The design of the EoR-Spec FPI was created by PhD student Rodrigo Freundt and is based 

on a flexible parallelogram driven by stepper motors (Figure 19).  Some of the goals of my work 

on this project include answering the following questions: What stepper motor, gears and screws 

should we use for the EoR-Spec tip-tilt mechanism instrument? What is the impact of friction, 

temperature, and material selection on the chosen gears? Are our current calculations for the 

resultant force and torque on the gears and screws in the 4K environment, correct? The goal of 

asking these questions is to ensure the stepper motors produce the right amount of torque and force 

for moving the FPI. Some of the parameters we needed to consider while answering these questions 

include operational friction at low temperature (4K), material properties, validation of the applied 

equations, and the size constraints.  

 



37 
 

Stepper motors 

The first thing to question is why are we using a stepper motor instead of a Piezoelectric 

Transducers (PZTs)? The FPI spacing needs to change from 0.74 mm to 1.5 mm to observe various 

wavelengths as we scan from z ~ 8 to 3.5 (210 GHz to 420 GHz).  In the past, we have used PZT’s 

to drive far-IR FPI.  PZT’s can achieve extremely high accuracy but typically have limited range.   

The 0.76 mm travel range requirement is too large for any PZT that is physically small 

enough to fit into the available space for the FPI.  Fortunately, in our case, since the step size needs 

to be only about 1/10th the resolution element of the FPI, stepper motor driven stages can achieve 

the required accuracy when a worm gear and fine adjustment screw is being used to perform the 

scanning. The FPI parallelism also needs to be adjusted to similar levels of precision, so we use 

stepper motors for tip/tilt adjustments as well. 

 

 

 



38 
 

 

 

 

 

 

  

 

 

Figure 19: CAD model of the EoR-Spec FPI [9].  The drive mechanisms involve cryogenic stepper motors.  

The top left image is a zoom in to the stepper motor, the worm and wheel gear drive. The top right image 

shows all three stepper motors and their placement within the FPI housing. The bottom left and right images 

show the flex vane (green), the tip-tilt stage (yellow), the plate to which the moving/scanning mirror is 

being attached (pink) and the outer fixed box frame (various shades of gray).  

 

Stepper motors have their own set of advantages in addition to being able to move the 

required range of motion. For example, the calibration process is simpler because the motors move 



39 
 

in very well-defined fractions of a rotation based on their step size. The rotational step is translated 

into linear movement through our gear to fine adjustment screw chain.  One then can calculate the 

distance that the adjustment screw moves by knowing the gear reduction, the threads per inch on 

the fine adjustment screws, and the number of steps made by the motor.  

The use of stepper motors also has some drawbacks. While the FPI will only be moved 

during intervals between observations, stepper motors produce much more vibrations and heat 

compared to PZTs.  At low temperatures, heat capacities are low, so the generated heat must be 

dissipated quickly so that it does not add to the thermal background on the detectors. Additionally, 

stepper motors can in principle contribute electromagnetic noise to the system. Therefore, we will 

not move the FPI while collecting data. [10] 

Our goal is to ensure that the stepper motors produce the proper amount of torque for 

rotating the fine adjustment screw and effecting the required travel of the mirror translation stage. 

This is best achieved through the implementation of worm and worm wheel gearing into the system 

(Figure 20).  

 

Figure 20: This is a worm for worm gear from PIC design.  Q2-1 (pic-designcatalog.com) 

 

 

 

https://www.pic-designcatalog.com/q2-1.html?action=3D


40 
 

Results - fine adjustment screw and worm gear drive: calculations and considerations on 

friction, diameter, and force 

The fine adjustment screw and worm gear drive play a crucial role in the FPI precision of 

movement.  This chapter discusses the calculations, values, and derivations for the fine adjustment 

screw’s worm gear drive to input into the Excel model. The purpose of these calculations is to 

determine what materials to select and to ensure our designs will function properly. Previous work 

on this topic was done by Ellen Lee. 

An initial Excel model of the fine adjustment screw and worm gear drive was completed 

by Thomas Nikola. There were some changes made to the model. Specifically, the friction values, 

thermal contraction, material properties, and an equation were modified after re-deriving the 

formulae and values.  

After the Excel sheet was checked and modified, a final table was created to show the 

resulting material properties, torques, and forces on the fine adjustment screw and worm gear 

drive. This table automatically updates when the inputs change.  

Friction coefficient and temperature dependence 

We will likely choose the materials stainless on phosphor bronze for the worm and gear 

drive to minimize the effects of friction.  Stainless steel is a usual choice for many mechanical 

applications but because stainless on stainless steel can stick or fuse at cryogenic temperatures, we 

picked stainless on phosphor bronze to minimize the effects of friction while refraining from using 

the same material for both worm and wheel. Specific focus was given to investigating friction and 

temperature for the worm and wheel. Usually, the purchased materials come with data 

specification sheets. However, the unknown factor was how the material would perform after being 



41 
 

cooled to 4K. So, we investigated friction at cold temperatures. We assume that the gears will 

operate with no lubrication.    

First, we address the coefficient of friction, μ. At room temperatures, a friction coefficient 

value of 0.35 is commonly used between 303 Stainless Steel and 510 Phosphor Bronze materials. 

The decision to use the μ = 0.35 value was based on both a NASA list, which states the friction as 

0.34, and the "Machinery's Handbook," which lists the friction as 0.35 for dry static friction. There 

are other options that are also worth considering and they are depicted in the table below (Table 

3). [11] We investigated a variety of metals against other metals and listed the ones we 

investigated.  These values are different than the original values listed in Ellen Lee's paper which 

suggested a friction value of 0.51.  

Table 3: Friction Coefficients for EoR-Spec gear drives 

Material 

combination 

Type of friction Value of μ 

Mild-steel against 

phosphor bronze 

Sliding/dry 

coefficient of friction 

0.34 [12] [13] 

Phosphor bronze 

against steel 

Static/dry coefficient 

of friction 

0.35 [14] [15]   

Steel against brass Static/dry coefficient 

of friction (min, max) 

 0.51 [16] 

Steel against brass Static/dry coefficient 

of friction 

0.51 [17] 

 

Table 3: This table depicts the different materials that we investigated for worm and gear combinations. 

We ultimately decided on the first one, mild steel against phosphor bronze, due to its low coefficient of 

friction. We do not want to use the same material due to the potential to stick at cryogenic temperatures.  

 

Regarding the effect of temperature on friction, I found conflicting information. Most of 

the time, friction values are experimentally determined, and cryogenic values are rarely reported. 

However, some fundamental physics articles proposed potential decreases in the friction 

coefficient, μ, as temperatures approach absolute zero (0K) due to a temperature dependance, 



42 
 

dipole-dipole interaction component of the Van Der Waals forces. At extremely low temperatures 

near absolute zero (0K), the reduction in thermal energy limits the strength of van der Waals forces, 

potentially resulting in decreased friction. [18] 

To further investigate the interaction between friction and temperature between 303 

Stainless Steel and 510 Phosphor Bronze, a specific paper, “Frictional properties of structural steel 

JN2 at cryogenic temperatures in a vacuum” by A Iwabuchi shows minimal correlation between 

temperature and friction in this specific case of JN2 structural steel and Bronze (CuSn). These 

materials are very similar to the 303 Stainless Steel and 510 Phosphor Bronze materials. As friction 

coefficients must be experimentally determined, we decided to utilize the room temperature value 

of 0.35 for both warm and cold conditions in the calculations. 

Fine adjustment screw diameter at different temperatures 

It is necessary to compare the fine adjustment screw’s diameter relative to the worm gear 

at warm and cold temperatures (4K) to ensure the differential shrinkage will not prevent the device 

from working. The screw diameter is 6.35 mm when warm and 6.34 mm when cold.  

Likewise, the length of the screw will shrink. It is assumed that the screw material shrinks 

uniformly. Because of this shrink, the threads per inch also change with temperature. We would 

expect there to be more threads per inch when cold than warm. Also, assuming uniform shrinking 

in the same materials, we do not expect the angle to change, just the threads per inch.  

Force on the screw 

The complete derivation of the torque and force on the screws were double-checked and 

re-derived. The simplification of the derivation for the final torque on worm along with the final 



43 
 

equation of the torque on the worm are shown (Figure 21). In this figure on the top, we have two 

gears. Ignoring friction, we have: 𝜏1𝑟1= 𝜏2𝑟2, where 𝜏1 is torque on gear one and 𝑟1 is radius of 

gear 1, same for gear 2. When we replace gear 1 with a worm, as shown in the bottom drawing, 

the geometry becomes a bit different, but the equation should still hold true when modified using 

geometric analysis to include a function f:  𝜏1𝑟1= 𝜏2𝑟2 ∙ 𝑓(Ø, 𝜆, 𝜇)  that depends on three specific 

characteristics of the worm: the pressure angle, lead angle, and friction. Now, with the worm 

instead of the gear, the names of these symbols change. 𝜏1 => 𝜏𝑤 (torque of the worm), 𝜏2 => 𝜏𝑔 

(torque of the gear), 𝑟1 => 𝑟𝑤 (radius of worm) and 𝑟2 => 𝑟𝑔 (radius of gear) and we can solve just 

for the torque on the worm. 𝜏𝑤  = 𝜏𝑔. 
𝑟𝑔 

𝑟𝑤 
  

𝒄𝒐𝒔Ø𝒔𝒊𝒏𝝀− 𝝁𝒔𝒊𝒏𝝀

𝒄𝒐𝒔Ø 𝒄𝒐𝒔𝝀− 𝝁𝒔𝒊𝒏𝝀
  This equation includes the function f, 

which was checked against textbook derivations and used in Excel. It was used to produce the 

values below (Table 4).  

 

Figure 21:  This is a simplification of the derivation for the torque on worm wheel equation.  

The maximum torque anticipated is 0.00718 Nm, corresponding to a 5.4 N force applied 

to the screw. I calculated many different values of the force and torque, and I considered the highest 

 𝜏𝑤    𝜏𝑔. 
𝑟𝑔 

𝑟𝑤 
  

𝒄𝒐𝒔Ø𝒔𝒊𝒏𝝀− 𝝁𝒔𝒊𝒏𝝀

𝒄𝒐𝒔Ø 𝒄𝒐𝒔𝝀− 𝝁𝒔𝒊𝒏𝝀
    



44 
 

nominally predicted value of 5.4 N and included it in the relevant table. To be conservative, also 

included in the table are the values of 6.2 N used by Ellen Lee and double that value (12.4 N).  

Table 4: Forces and Torques 

Table 5: Input Values 

Tables 4 and 5: Table 4 from an Excel spread sheet contains the predictive torques, both when at 

room temperature (orange columns) and when cold at 4K (blue columns) to effect various 

amounts of force on the screw. The highest nominally predicted value of force on the screw is 

5.4N. Table 5 depicts the changeable inputs for the chart outputs.   



45 
 

Discussion 

In conclusion, the calculations for the fine adjustment screw's friction, diameter, force, and 

torque have been re-derived and thoroughly checked. By using a conservative approach and 

considering temperature effects, we can confidently model and predict the reliability and 

functionality of the fine adjustment screw in various conditions. Here, the calculations show that 

the expected torques are smaller than those that the stepper motor we have chosen for our project 

can provide, so the stepper motor should work. The initial Excel model was revised resulting in a 

more realistic model of what forces might be encountered.  

Some limitations to this model include the fact that the friction can be difficult to model 

because of not fully determined properties at low temperatures. Also, the efficiency of the motor 

might decrease as it gets cold, and there might be difficulties with the electronics. The next step is 

to purchase the components and to test them in the laboratory.  

CHAPTER IV 

CONCLUSIONS AND FUTURE WORK 

 

For the project 

The Tip-Tilt mechanism has been designed using SolidWorks and gear types have been 

selected. The next step is getting a tunable FIR laser which will make this measurement 

significantly easier.  

For the VIPA, a schematic POEMM protoplanetary disk model was developed for 

visualization.  Much more sophisticated models exist in literature and are being developed by 



46 
 

members of the POEMM and FIRSST science teams. We have tested the POEMM VIPA in the 

lab. While the first tests were not successful, very recent tests with a QCL were successful. The 

next steps for this project are that we won a new APRA grant for space and balloon-borne VIPA 

spectrometer development which will be paramount for development of the POEMM and 

FIRSST missions.  

For EoR-Spec, the gear calculations were derived and completed. Some values changed 

from previous work. Forces and torques were derived, accounting for various parameters for 

EoR-Spec. The next steps include using my calculations to decide on what gears and motor to 

purchase for testing the EoR-Spec FPI system.  

The completion of my Master's thesis in astronomy and space sciences has sharpened my 

analytical skills and deepened my understanding of space sciences and instrumentation. This 

academic endeavor has not only honed my ability to tackle complex scientific problems but has 

also instilled in me a curiosity for applying these skills in real-world contexts.  

For me personally     

While it was a difficult decision to leave the PhD program, I believe it is the right choice 

for me. As I transition from academics into consulting, I am confident that I can succeed in 

combining my science and business skillsets to solve challenges at the intersection of space, 

science, and business innovation. I am particularly excited about the prospect of encountering 

novel problems and gaining exposure to a wide array of intriguing projects, while contributing 

meaningfully to the evolving landscape of scientific exploration.  

There are some missing links between the opportunities that await us in space sciences and 

the ability to facilitate them with the required funding, business acumen, and entrepreneurial drive 



47 
 

needed to successfully execute. With my consulting career, I hope to actively participate in the 

business of space, nurturing the growth of this industry and supporting groundbreaking projects 

through enabling entrepreneurship, strategic funding, and enhancing science communication to 

both the industry and the public. I believe Cornell has armed me well with the tools and skills I 

need to truly make a difference and I thank each of you for personally helping me in this journey. 

In the future, I look forward to learning from the challenges and opportunities that my career will 

bring, while knowing that I am armed with the lessons gained from my time in this academic 

program. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



48 
 

BIBLIOGRAPHY 

 

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[3] Born, Max, et al. *Principles of Optics*. Cambridge University Press, 2019. 

 

 

[4] Kitchin, Christopher Robert. *Astrophysical Techniques*. CRC Press, 2020. 

 

 

[5] Sakai, Kiyomi. "Far Infrared Metal Mesh Filters and Fabry-Perot Interferometry." *Reviews 

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49 
 

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