P17618: Lens Handling Fixture
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Systems Design

Table of Contents

Team Vision for System-Level Design Phase

The System Level Design Phase is intended for the team to research system related physics, current solutions, and system functions that will help facilitate the brainstorming of concepts. Fully defining the project scope and identifying all system functions through the use of functional decomposition is meant to better understand project requirements and assess plausibility. Benchmarking and feasibility analysis are two of the possible approaches to aid in concept generation and identifying key improvements that can be made to functions. Our team plans to complete these actions in order to help select a final concept, where more in-depth analysis, simulation, prototyping, and designing can be completed in order to develop the most effective solution to the problem.

At the completion of this phase, it was evident that research played a pivotal role in helping to understand how the key functions of the solution can be performed, as well as how the underlying physics affect the possible solutions. Using this research, many concepts were generated for each function the system was to perform. Assembling function concepts into design concepts through the use of a morphological chart allowed the use of a Pugh chart to compare generated concepts to each other and also to existing solutions. A final concept was generated and now the team can continue with system architecture analysis and further improvements from the design process.

Technician Interviews and Updated Customer Requirements

We updated the customer requirements based on our performed customer interviews which showed substantially that a need for a new horizontal interferometer configuration outweighed the need for a vertical interferometer fixture. See picture below for a summary of the information gathered from the technician interviews. The information is proprietary and can only be accessed by definitive parties.
 Summary of all Technician Interviews

Summary of all Technician Interviews

The full customer complaints document can be access here: //private/CustomerComplaintsFull.xlsx.

Going back to the customer requirements, we learned that it was more important to develop a horizontal solution for only lens shapes (not rectangular or square) rather than a vertical solution. We also need to reduce the amount of material waste compared to the current solutions available. The current fixtures are also lacking a way to rotate the lens freely for the testing requirements.

 New Customer Requirements after Technician Interviews

New Customer Requirements after Technician Interviews

We also used this information to perform the following process steps: functional decomposition, morph chart, and concept development.

Functional Decomposition

The functional decomposition moves in a why to how fashion, a top to bottom approach of whys and how’s? The goal of the functional decomposition is to match the main customer requirements to specific functions that the fixture we will design needs to perform.

 Functional Decomposition: Match customer requirements to functions.

Functional Decomposition: Match customer requirements to functions.

List of Customer Requirements summed to Functions:

The main functions and focuses in the group currently are highlighted in yellow and are listed below:

Other necessary considerations include:

We also strive to incorporate:

By completing the Functional decomposition, we achieved a much more focused approach on how to obtain the end goal and how each sub-function played into our overall intention. This allowed us to create a list of functions and sub-functions based on the customer and engineering requirements. The functional decomposition acts as a guide for benchmarking, and ultimately, concept generation.

Benchmarking

The goal behind benchmarking was to find other products, companies, and ideas that solve the problem of two of the highlighted functions in the functional decomposition: secure the lens, neutralize stress. The table below shows the results of our benchmarking for looking at the current types of radial mounts available in the marketplace.
 Benchmarking: Look for outside inspiration from marketplace.

Benchmarking: Look for outside inspiration from marketplace.

Sources:

[1] Schwertz, Katie and Burge, James. Field Guide to Optomechanical Design and Analysis, Vol. 26. SPIE Press, 2012, pp. 82.
[2] Yoder, Paul and Vukobratovich, Daniel. Opto-Mechanical Systems Design: Design and Analysis of Large Mirrors and Structures, Fourth Edition, Vol. 2. 4th ed. CRC Press, 2015, pp. 121-123.
[3] "AOM130M Series Optical Mounts & Gimbals | Aerotech, Inc.", Aerotech.com, 2017. [Online]. Available: https://www.aerotech.com/product-catalog/gimbals-and-optical-mounts/aom130m.aspx. [Accessed: 06- Mar- 2017].
[4] "AOM110 Series Optical Mounts | Aerotech, Inc.", Aerotech.com, 2017. [Online]. Available: https://www.aerotech.com/product-catalog/gimbals-and-optical-mounts/aom110.aspx. [Accessed: 06- Mar- 2017]
[5] E. Inc., E. Inc. and E. Inc., "Precision Pinhole Mount", Edmundoptics.com, 2017. [Online]. Available: https://www.edmundoptics.com/optomechanics/optical-mounts/iris-aperture-mounts/precision-pinhole-mount/2001/. [Accessed: 03- Mar- 2017].
[6] C. Gal ; A. Reutlinger ; A. Boesz ; T. Leberle ; A. Mottaghibonab ; P. Eckert ; M. Dubowy ; H. Gebler ; F. Grupp ; N. Geis ; A. Bode ; R. Katterloher ; R. Bender; Test results of high-precision large cryogenic lens holders. Proc. SPIE 8450, Modern Technologies in Space- and Ground-based Telescopes and Instrumentation II, 84500P (September 13, 2012); doi:10.1117/12.926860.
[7] E. Inc., E. Inc. and E. Inc., "Precision Pinhole Mount", Edmundoptics.com, 2017. [Online]. Available:https://www.edmundoptics.com/optomechanics/optical-mounts/optical-lens-mounts/optical-cell-assemblies/1798/. [Accessed: 06- Mar- 2017].
[8] E. Inc., E. Inc. and E. Inc., "Precision Pinhole Mount", Edmundoptics.com, 2017. [Online]. Available: https://www.edmundoptics.com/optomechanics/optical-mounts/optical-lens-mounts/english-bar-type-holders/1688/. [Accessed: 06- Mar- 2017].

The full benchmarking document can be found here.

Morphological Chart

After completing the benchmarking phase, we combined the functional decomposition, our benchmarking, and other research to create a Morph Chart. A morph chart allowed us to imagine/observe parts that would perform the functions in the functional decomposition.

 Morph Chart: Match functions and benchmarking.

Morph Chart: Match functions and benchmarking.

Concept Development

After we created the Morph Chart, we used it to incorporate ideas and form multi-variable concepts.

(Note: At this step, the logistics of the combinations are not taken into account.)

 Concept Generation Cycle 1

Concept Generation Cycle 1

 Concept Generation Cycle 2

Concept Generation Cycle 2

Concept Selection

Now that we had preliminary designs in order, we analyzed those designs by using a Pugh Chart. The Pugh Chart is a grading system for each design when matched against the customer requirements to see which concept provides the best solution.

 Pugh Chart: Process for deciding between ideas.

Pugh Chart: Process for deciding between ideas.

The full Pugh chart can be found //public/Systems Level Design Documents/PughChartFull.xlsx

Feasibility: Research

Now that we have our initial concepts and design selected, we can ask the question, "is our preliminary design going to work? How are we going to confirm that our design is going to work?"

Materials

In order to understand what kind of materials and material properties we should be looking for in our design, our time decided to dedicate our time researching different type of materials which could be useful in our design.
 Pugh Chart: Process for deciding between ideas.

Pugh Chart: Process for deciding between ideas.

How to Quantify Stress in Large Lenses?

During the technician interviews, it was understood that the most significant part of the customer requirement of achieving no stress in the lens was trying to overcome the deflection due to gravity in a lens. In order to better understand this phenomenon, the team decided to perform some research into gravity self deflection of a lens.

Conceptual Mathematical Models for Self Deflection due to Gravity

In order to conceptually design a system, we first needed to understand, "what mathematical or physical models exist which quantify the problem at hand?"

 Mathmatical Models for Gravity Self Deflection

Mathmatical Models for Gravity Self Deflection

Note: For thick mirrors with aspect ratios between 7 and 10, the deformation from shear effects is about 4% of the total portion deflection. Therefore, it will be neglected to perform a first order analysis.

Source: Yoder, Paul and Daniel Vukobratovich. Opto-Mechanical Systems Design: Design and Analysis of Large Mirrors and Structures, Fourth Edition, Vol. 2. 4th ed. CRC Press, 2015, pp. 117.

We have decided to use 'Schwesinger's' Mathmatical Model for self deflection because it is the simplest model, and most commonly used method. As well as the fact that we are mostly going to be working with lenses with aspect ratios between 6 and 8, so the first order analysis should be good enough.

Schwesinger Schematics

 Schematic Horizontal Gravity Self Deflection

Schematic Horizontal Gravity Self Deflection

The schematics above are provided by Schwesinger and show the radial boundary forces due to gravity on a uniform thickness and concave mirror.

For a uniform thickness mirror, or a symmetrical mirror, there are only tension and compression forces acting within the mirror in order to keep the mirror in static equilibrium. However, when you have a concave or convex mirror, the non-uniform thickness causes a bending moment to be applied to the lens by gravity.

In order to determine the magnitude of this bending moment, Schwesinger constructed the following free body diagram.

Free Body Diagrams

 Free Body Diagram of Bi-Convex and Bi-Concave Mirrors

Free Body Diagram of Bi-Convex and Bi-Concave Mirrors

The free body diagram above shows that Bi-Convex and Bi-Concave mirrors are symmetrical about their midplane, so gravity affects them in the same way as a uniform thickness mirror. In a uniform thickness mirror, no external bending moments are applied to the lens due to gravity.

 Free Body Diagram of Convex and Concave Mirrors

Free Body Diagram of Convex and Concave Mirrors

The free body diagram above shows an element "dW" of force causing an elemental bending moment to the lens. By solving for the moments around the midplane.

We discover the magnitude of the bending moment applied to the fixture by gravity.

 Magnitude of bending moment

Magnitude of bending moment

For Concave-Convex lenses, in order to determine the bending moment applied to the surface due to gravity, the shape will be modeled by two equal semicircles cut and added to a rectangle. A free body diagram of the concave-convex lens as follows.

 Free Body Diagram of Concave-Convex i.e. approximation Meniscus lenses

Free Body Diagram of Concave-Convex i.e. approximation Meniscus lenses

Therefore, by taking the bending moments around the midplane, we realize the bending moment is twice that of a concave or convex lens.

 Bending moment calculations for Concave-Convex lenses

Bending moment calculations for Concave-Convex lenses

In conclusion, in order for our fixture to provide "no stress" to the lens, we need to be able to provide a bending moment to convex, concave, and convex-concave lenses.

Source: Yoder, Paul and Daniel Vukobratovich. Opto-Mechanical Systems Design: Design and Analysis of Large Mirrors and Structures, Fourth Edition, Vol. 2. 4th ed. CRC Press, 2015, pp. 116-117.

Quantifying Deflection

In order to try to confirm our mount works as expected, we need a quantifiable measurement to answer the question of "how much stress does the mount apply to the lens by holding it?"

The wavefront error shown by a lens is proportional to: the error caused by inducing stress in the mount, the error due to aberrations in the mirror, and environmental factors such as temperature.

Robert Royce, "Testing Telescope Mirrors and Statement of Standards," R.F. Royce - Precision Optical Components. Available: http://www.rfroyce.com/testmethod.htm. [Accessed: 02/20/2016].

In order to answer this question, Schwesinger quantified stress deformations in terms of wavefront error. Wavefront is the difference between an ideal wavefront and the actual wavefront measured in terms of wavelength of light.

 Wavefront Visual Representation

Wavefront Visual Representation

Austin Roorda. Class Lecture, Topic: "Review of Basic Principles in Optics, and Wavefront Error". University of California, Berkeley, CA. Website: http://voi.opt.uh.edu/VOI/WavefrontCongress/2006/presentations/1ROORDAprincip.pdf

The wavefront error is proportional to "how much stress" is caused by the mount. In other words, "The rms departure from perfection (in waves) of the wavefront reflected from a gravitational deformed horitzontal-axis mirror' is as follows.

 Equation for Wavefront Error

Equation for Wavefront Error

Source: Yoder, Paul and Daniel Vukobratovich. Opto-Mechanical Systems Design: Design and Analysis of Large Mirrors and Structures, Fourth Edition, Vol. 2. 4th ed. CRC Press, 2015, pp. 120.

Schwesinger Experimental Setup

In order to confirm the theoretical "Ck" value above, Schwesinger performed the following experiment with

Overall Procedure

 Calculation K value

Calculation K value

He set this property because he needed a way to keep the size of the lenses he was testing relatively the same. Since gravity affects depend on the shape of the lens, it makes sense to keep the "K" same throughout the experiment.

He also wanted to be able to relate "K" easily to the f# of a lens because, that is more often than naught, listed on a spec sheet then aspect ratio. So, this is why he set the relation D = 8t.

Relating K to f#

Relating K to f#

If you need a refresher on what the f# is:

 Definition f# of a lens

Definition f# of a lens

 Experimental Results

Experimental Results

Source: Yoder, Paul and Daniel Vukobratovich. Opto-Mechanical Systems Design: Design and Analysis of Large Mirrors and Structures, Fourth Edition, Vol. 2. 4th ed. CRC Press, 2015, pp. 121-123.

A man named Vukobratovich then came in and performed an experiment which extrapolated the Ck value for different values of K (not just D = 8t) based on a parabolic curve fit. He confirmed his values of Ck to Schwesinger.

 Vukobratovich Approximation

Vukobratovich Approximation

Sources: Schwertz, Katie and Burge, James. Field Guide to Optomechanical Design and Analysis, Vol. 26. SPIE Press, 2012, pp. 82.

Yoder, Paul and Daniel Vukobratovich. Opto-Mechanical Systems Design: Design and Analysis of Large Mirrors and Structures, Fourth Edition, Vol. 2. 4th ed. CRC Press, 2015, pp. 121-123.

This is the equation you will see in the "Field Guide of Optomechanical Design and Analysis". The constants a0, a1, and a2 are fitted to experimental results.

Ideal Mount

From the table 3.1 above, you might be asking "What is this "Ideal Support" that Schwesing is referring to?"
 Ideal Radial Mount

Ideal Radial Mount

Yoder, Paul and Daniel Vukobratovich. Opto-Mechanical Systems Design: Design and Analysis of Large Mirrors and Structures, Fourth Edition, Vol. 2. 4th ed. CRC Press, 2015, pp. 127.

All of the horizontal mounts have been trying to replicate the "ideal" force diagram above taken from an analytical simulation called "Dynamic Relaxation" created by Malvick and Pearson (1968).

The main takeaway from the diagram above is that the tensile and compression forces vary with the cosine of the polar angle measured from the vertical axis on the mirror.

In order to confirm our lens mount was to works exactly like an ideal mount, we would use a lens similar to the one used in Schwesinger's experiment, measure the rms deflection (in waves), and obtain the "Ideal Support" values for Ck listed in Table 3.1

Experimental Calibrated Ronchi Test

Now, you may be thinking, "when Schwesinger measured the wavefront error in his mounts, how did he know that the deflection was from the mount and not from the defects in the lens itself?" The truth is I don't know yet. I haven't read Schwesinger's and Vukobratovich's specific experimental papers yet.

However, while I was searching for a way to answer this question, I came upon a testing method called the "Ronchi Test". The "Ronchi Test" is primarily used to quantify spherical aberration and astigmatism caused by a mount. Other abberations such as defocus, coma, and tilt are ignored in the processing of the test. The "hand wavy" procedure for the "Ronchi Test" is listed below.

  1. Load lens in fixture and assume this to be 0 degree of rotation.
  2. Take a set of 10 pictures with the interferometer, and average these pictures together.
  3. Rotate the lens by 90 degrees. If the aberration, such as astigmatism, is observed stays in the same place, this is likely the astigmatism caused by the mount. Take another set of 10 pictures with the interferometer and average these pictures together.
  4. Repeat step 3 for 180 degrees, and 270 degrees.
  5. Assuming that the astigmatism is the same value for each of the rotation positions in the mount, you can average all of the 40 "wavefront" maps taken. By doing this, you effectively "cancel out" the astigmatism due to the mount and leave only the mirror astigmatism. See picture below for more information.
 Experimental Process Visually

Experimental Process Visually

The purple line represents the astigmatism in the lens caused by the mount at a particular position. Since all four pictures are mirror images of each other, the astigmatism due to the mount cancels out.

In order to determine the mount astigmatism specifically now, you can:

Royce, Robert. "A Better Method Of Measuring Optical Performance". Rfroyce.com. N.p., 2017. Web. 5 Mar. 2017.

Conclusions about Design

We cannot get you "absolutely no stress" because even interferometers have measurement error. However, we can:

Risk Assessment

Our original goal was to have a final concept selected by the Systems Level Review. However, after much hard work performed by the team, we realized we needed to spend more time in our concept development phase to ensure that our design will perform the customer requirements.

In order to mitigate the time loss, we have decided to move into the prototyping phase during the Detailed Design Phase in order to test the feasibility of our design early.

 Risk Management Version 1

Risk Management Version 1

This document will be progressively updated through the next stages of Senior Design.

The full Risk Management document can be found here.

Plans for next phase

By the next review, our team plans to develop and produce a scale working prototype of the concept that can be used functionally with a workpiece. The prototype is meant to demonstrate the loading support necessary to achieve acceptable stress in the workpiece. Through this, we hope to have quantitative data measuring the effectiveness of the chosen design in mitigating stress in the workpiece. Having a comparable figure will allow us to better understand how the system is performing in comparison to other solutions and can offer insight into potential improvements. Additionally, having preliminary computer drawings or models can help define the concept more concretely, and allow for hands-on analysis that is otherwise unavailable through simple sketches. Having simulations of the concept can further aid in structural and functional analysis and feasibility for iterative review and improvements.

Questions to be Answered by the Next Review:

  1. How effective is the design at mitigating stress? Is this quantifiable?
  2. What numerical analysis or simulations were performed to model the behavior or performance of the design?
  3. Will there be a preliminary physical prototype to present?
  4. What steps have been taken to help facilitate manufacturing at the larger scale? Has a Bill of Materials been completed?
  5. Are the proposed materials readily available and plausible to use?
  6. Are there plans developed to test the concept performance?
  7. What major risks have been identified and how can they be mitigated?
  8. Are there mitigation or back-up plans in place?

Using the team’s individual 3-week plans, we have outlined the next steps to be taken to achieve these expectations. Outlined below are the individual plans for review:

Individual 3-week plans:

Carrie
Derek
Emily
Matt

We have also updated the Project Plan to show to the expected progress of the project.

Updated Project Plan

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