Design Description Document · Web viewA Rubens’ Tube design for use with water. Light scattering off of silica beads in the tube will help illustrate standing wave pattern. A subwoofer

The Rochester Museum and Science Center Prototypes

University of Rochester

Design Description Document

RMSC Exhibit Prototypes

David Kim, Kara Morse, Madhu Ashok, Rebecca Pettenski

Customer: Calvin Uzelmeier (RMSC)Engineers: David Kim, Kara Morse, Madhu Ashok, Rebecca PettenskiAdvisor committee: Wayne Knox, Joseph Choi

Document Number: 002

Revision Level:B

Date: 5/16/2023

This is a computer generated document and the electronic master is the official revision. This paper copy is authenticated for the following purpose only:

Authentication Block

Four individual exhibit prototypes able to engage families with children ranging from 5-13 years old. The exhibits include: “Rochester Cloaking”, “LED Rubens’ Tube”, “Cell Phone Magnification Fun”, and “Schlieren Photography”.

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ContentsProduct Requirement Document.................................................................................................................3

LED Rubens’ Tube........................................................................................................................................3

Optical Design 1.......................................................................................................................................3

Optical Design 2.......................................................................................................................................4

First Order Analysis / Photon Budget......................................................................................................4

Test Plan..................................................................................................................................................6

Risk Assessment......................................................................................................................................7

Cloaking Device.........................................................................................................................................10Cell Phone Magnification...........................................................................................................................23Schlieren Imaging System..........................................................................................................................25

References.................................................................................................................................................28



Product Requirement Document (See digital document 001)

LED Rubens’ Tube1) Optical Design 1: Operation with smoke2) Optical Design 2: Operation with water3) First Order Analysis4) Test Plan 5) Risk Assessment

Optical Design 1Operation with smoke: This needs to be further tested and validated

Overview:

A Rubens’ Tube design for use with smoke generated from a mister or a fog machine. Scattering will be visually displayed with a collimated laser source or an LED bar underneath the tube. The speaker used for created sound waves will be a subwoofer for maximum air displacement.

Figure 1 – Optical Design 1



Optical Design 2Operation with water: This still needs to be tested

Overview:

A Rubens’ Tube design for use with water. Light scattering off of silica beads in the tube will help illustrate standing wave pattern. A subwoofer for maximum air displacement (at higher amplitude due to the increase in density).

Figure 2 – Optical Design 2

Optical Design 3Operation with Water Vapor and Open Ended Tube

Overview:

A Rubens’ Tube design for use with water vapor with an input from an open ended tube. Scattering is observed through the use of 3 parallel beams created from a 633nm HeNe laser. The beam from the laser source will be split using two beam splitters. In this prototype the water vapor emitted from the



spouts vary in cone angle with pressure inside the tube. Low pressure in the tube corresponds to higher velocity through the spouts, and a smaller scattering area with the HeNe beams.

Figure 3: Optical Design 3

First Order Analysis / Photon Budget Acoustic reflection is modeled by an equation similar to optical reflection, where index of refraction is substituted with the acoustic impedance (at normal incidence):

R=(Z2−Z1Z2+Z1 )2

MaterialAcoustic Impedance (g/ s*cm^2)

Water 1.48E+05Acrylic Resin 3.15E+05Aluminum 1.71E+06Steel 4.54E+06Air 4.15E+04

Figure 3 – Table of Acoustic Impedance measured in ( gcm2×s ) for various materials [1].

Optical Design 1: Smoke Smoke-Aluminum Interface

R=( 1.71E+06−4.15E+041.71E+06+4.15E+04 )2

R=90.75%



Smoke-Steel InterfaceR=96.40%

Optical Design 2: Water

Water-Aluminum InterfaceR=70.68%

Water-Steel InterfaceR=87.77%

Optical Design 3: Water Vapor

The current design has an open ended tube, so there is no reflection. If an interface was implemented the reflection would be near identical to optical design 1.

The fundamental frequency of the tube will determine the lowest frequency for a standing wave pattern to be displayed in the spouts. Given a fixed tube length with an acoustic reflector on the end, the problem models a closed-end air column:

Figure 4 – Closed-end air column illustration of the first harmonic (quarter wave). The reflection causes a standing wave pattern when the length of the tube (L) is a fourth of the wavelength [2].

f 1=vλwhere λ=4 L f 1=

v4 L

Given a fixed tube length with an open end, the wavelength corresponds to half of that in the closed-end problem. This occurs due to the lack of the reflection on the end of the tube.

Figure 5- Open-end air column illustration of the first harmonic (half wave). An antinode will exist at the end of the tube [3].

Similarly the fundamental frequency for an open ended tube follows the equation:

f 1'=vλwhere λ=2L f 1'=

v2 L



Optical Design 1: SmokeThe speed of sound in air is approximately 343 m/s, which is a slight underestimate for the

speed of sound in smoke/water vapor. This difference is minimal compared to the effects of pressure differences in the standing wave at the various spouts. The tube length is fixed at 3 feet (.91 meters)

f 1 s=3434∗.91 f 1 s=94.23Hz

This is a rough estimate of the frequency required to have a quarter wave displayed on the spouts (the resolution of this pattern will depend on the number of spouts).

Optical Design 2: WaterThe speed of sound in water is approximately 1482 m/s. The tube length will be the same for

this problem, so the fundamental frequency will be different than in the smoke design.

f 1w=14824∗.91 f 1w=407.14Hz

Optical Design 3: Water VaporThe speed of sound in water vapor can be approximated by the speed of sound in air: 343 m/s.

The tube length is again fixed at 3 feet (.91 meters). The wavelength in this case is double the tube length.

f 1wv=3432∗.91 f 1w=188.46Hz

Initial testing of optical design 3 brought about a new illustration of inner-tube pressure. A flame tube will display higher flame peaks where there is low pressure in the tube, and lower flame peaks where the pressure is higher. Water vapor does not display this characteristic as simply due to dissipation of the vapor as well as the influence of air in the room. In the first round of testing the fan rate was increased to create equal spouts. The pressure differences were seen through variance in cone angle emitted from the spouts. This arises from volumetric flow rate:

Q=v∗AWhere Q is the volumetric flow rate, A is the cross sectional area, and v is the velocity of the water vapor. Velocity and pressure in the tube are inversely proportional, so low pressures inside the

tube correspond to higher velocities of the water vapor and smaller cross sectional areas. The scattering from the laser beams illustrate the cross sectional area.



Figure 6: Cross sectional area of water vapor flow illustrated through scattering. When low pressure exists in the tube there will be a higher velocity of the output vapor, and subsequently a smaller scattering cross sectional area.

Photon Budget:Let us assume Lambertian scattering, as well as an index of refraction of 1.33 for water vapor, 1.42 for silica beads, and 1.49 for acrylic [4].

Optical Design 1: SmokeThe photon path for an observer to see scattering is from the LED source through the acrylic,

reflecting off of the water vapor, and returning through the acrylic to the eye. This accounts for five interfaces.

( .96 ) ( .96 ) ( .03 ) ( .96 ) (.96 )=.025

Optical Design 2: WaterThe photon path for an observer to see scattering off of the silica beads is similar to the first

design. There are five interfaces: two air-acrylic interfaces, two water-acrylic interfaces, and a water-silica bead interface.

( .96 ) ( .997 ) ( .001 ) ( .997 ) ( .96 )=.00092

Optical Design 3: Water VaporThis design implements a 633nm HeNe beam split into 3 beams using two beam splitters. The

calculation will be different for the various beams. According to Thorlabs Catalog data on 50:50 cube beam splitters the p-polarized transmission is 45.9%, while the s-polarized transmission is 44.8% at 630nm [5]. Let us assume the mirrors reflect at 98% for both polarizations:



Beam1: ( .448 ) ( .98 ) ( .98 )=.4303Beam2: (.459 )(.448) ( .98 ) ( .98 )=.1975Beam3 : ( .459 ) ( .459 ) (.98 ) ( .98 ) (.98 )=.1983

Test PlanOptical Design 1: Smoke

1. The first step in testing will be to find the experimental fundamental frequency as accurately as possible. This test will be performed through a frequency range of 20Hz-20kHz. The first round of testing found f 1≈120Hz

2. Since repeatability is required for a successful exhibit at RMSC, the system will be tested with various amounts of smoke in the tube.

3. Next, a method for remotely filling the tube with smoke will be implemented.


1. Develop an acoustic reflector and membrane which can withstand the increased pressure with water.

2. Test various scattering in water with silica beads, glitter, creamer, etc.3. Develop a reservoir system to continuously supply water to the tube.


1. Develop an optical system with 3+ parallel HeNe beams.2. Create an isolated area for the spouts to decrease interference.3. Develop a moving mirror to illustrate a profile of the output smoke.4. Troubleshoot why frequency generator does not display high visibility.

Risk AssessmentOptical Design 1: Smoke

The main issues involved with this prototype revolve around the method of maintaining a constant flow of mist or smoke into the tube. Additionally, smoke from a fog machine leaves residue on the inside of the tube and sometimes blocks the holes.


The main issues involved with this design are the increased density of the medium inside the tube. This means the pressure inside the tube will increase. Introduction of water requires a higher displacement of volume from the speaker.




This prototype works great for displaying patterns with music, but when used for various frequencies shows poor visibility. Other problems that arose include blocking of the spouts, reflections off of the rubber membrane, pressure difference along the tube without sound, and overall low visibility of sinusoidal patterns. A flame tube shows pressure difference in an altogether different way, thus the patterns displayed vary. Instead of higher “flames” the output of smoke varies in output angle, with higher cone angles attributed to higher pressure in the tube (and lower velocity).

Rochester Cloaking

1st Order AnalysisFocal Length and Thickness Requirements

Requirementst1=(f1+f2)t2=2f2(f1+f2)/(f1-f2)OAL = 2t1 +t2 = 2f1(f1 + f2)/(f1 − f2)f1 = (1± √ 2)f2

Object and Image Positions

Afocal systemObject at infinityLens 1 and 2 act like Keplerian beam expanderCollimated light travels between lens 2 and 3Lens 3 and 4 act like Keplerian beam expander

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Image at infinityTotal magnification 1

Aperture (F/# & NA)

Entrance pupil is the objective lensF/# =f/EPDNA=nsinθ=nsin(0)=0

FOV

Entrance pupil is the objective lensF/# =f/EPD

Wavelength Region

Visible Light (~400-700nm)Material Choice: BK7

Entrance Pupil/Exit Pupil locations

Entrance pupil is the objective lens

3rd Order Analysis

Choose lens parameters, curvature, and index

Glass material undetermined (n unknown)

Bending Factor

c1 and c2 is curvature of the first and second surface of a thin lens. Note minimum when c1=-c2

Conjugate Factor

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Measure of object location with respect to lens.Lens 1 conjugate factor = -1Lens 2 conjugate factor = 1Lens 3 conjugate factor = -1Lens 4 conjugate factor = 1

G-Sums

Minimize spherical and coma through minimizing bending factor (c1=c2). On a side note, Joseph Choi reduces aberrations by using achromatic doublets.

Joseph Choi SystemSource: http://www.opticsinfobase.org/oe/fulltext.cfm?uri=oe-22-24-29465&id=304785

Joseph Choi’s current systemAchromatic doubletsLenses 1 & 4: 200mm focal length, 50mm diameter achromatic doublets BK7, SF2Lenses 2 & 3: 75mm focal length, 50mm diameter achromatic doublets SF11, BAF11Off the shelf Thorlabs lenses with anti-reflection coating. Note: these are the largest off-shelf achromats Thorlabs offers.Object distance 2m from first surface. Image distance 3m from last surface.Nominal wavelength (587.6nm)

Aberration valuesSpherical: 10.4Coma: -8.6

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Astigmatism: 8.2Petzval: 0.4Distortion: -8.47.7% for -1.5 degrees of field angle

Most aberrations occurred at the last two achromatsNo optimization used except achromats.

Optimize radius of curvature & airspaces to start.

MaterialsInitial plan to optimize with custom lenses is not possible. Budget constraints dictate that we use off-the-shelf components. After comparing catalogue optics from Thorlabs and Edmund Optics, we decided to use Thorlabs because it has cheaper prices for comparable spec optics. Note that although Edmund Optics offers lenses with larger diameters, they are significantly more expensive. All optics chosen are BK7 glass and have antireflection coating for wavelengths ranging from 350nm-750nm. Maximum diameter for biconvex-singlets are 50.8mm, for plano-convex singlets is 75mm, and for achromats is 50.8mm.

Notable comments from Joseph Choi’s paper include suggestions such as choosing a smaller total overall length (OAL). This reduces edge effects and increases the range of angles. Because OAL is dependent on focal length, it would be wise to choose the smallest focal length.

Both bi-convex and plano-convex lenses are tested in a set of 7 cases and 1 case of optimal achromats. Biconvex lenses are chosen because according to G-sums, they have the optimal curvature to reduce spherical aberration for a singlet. Plano convex lenses are chosen because they are the near-best-form shape to collimate light from a point source and focus collimated light to back focus. Also, they have the largest available maximum diameter, providing potential to create a larger system in height. They also bend the ray gradually for collimated light. This suggests that for the first surface, they should provide reduced aberrations. However, note that they do not minimize the bending factor in G-sums, suggesting that they will have more spherical aberration.

Take note that, like in Joe Choi’s model, aperture sizes are not restricted to ensure no vignetting.

Please access Results.xlsx for case properties.

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Case 123:46:46

CloakSinglets Scale: 0.25 DK 03-Mar-15

100.00 MM

Object angle ranges from ±0.75 degrees.

Case 2

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The Rochester Museum and Science Center Prototypes22:43:21


119.05 MM


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Case 322:48:27


125.00 MM


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Case 423:52:43


100.00 MM

Object angle changed to ±0.3 degrees.

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Case 500:48:06


125.00 MM


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Case 600:12:50


125.00 MM


Edge rays deviate from ideal path too much. Need to reduce object angle. This makes this case impractical.

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Case 700:55:41


138.89 MM


Edge rays deviate from ideal path too much. Need to reduce object angle. Design may be impractical

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Case 801:07:35

Test Scale: 0.20 DK 04-Mar-15

125.00 MM


ConclusionReferring to the table in results.xlsx, it is clear the two most prominent aberrations throughout all cases (1-8) are axial color and spherical aberration. Achromatic doublets helps reduce both of these aberrations. Under the conditions of a budget of $434.00 (not yet granted) this will be the optimal result in terms of aberration.

After achromatic doublets, biconvex lenses (cases 1-3) appear to be the superior setup to plano-convex lenses (cases 4-7). As expected by G-sums theory, biconvex lens setups have significantly lower spherical aberration than their plano-convex lenses counterparts. Axial chromatic aberrations remains similar for both. Biconvex lenses appear can operate under larger object angles. Judging by the criteria of the two most prominent aberrations and operational object angles, it appears that biconvex lenses are the optimal for sub $200 price range.

Also take note that in case 6 and 7, the edge rays do not go through the entire system. To avoid massive amounts of vignetting at such a small object angle range, it is best to avoid such as system.

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Taking Joseph Choi’s words of reducing overall length of the system, we should choose the smallest focal length. This points us to the 60mm focal length biconvex lens and 150mm focal length biconvex lens setup (case 1). To support his statement, case 1 has significantly less coma, tangential astigmatism, axial color, and lateral color than cases 2 and 3. It does have a slightly larger spherical aberration, but in almost all aberrations, it performs better.

Therefore, we decided to choose case 1 as our prototype lens.

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Cell Phone Magnification1) Design 1: Threaded Cylinder2) Design 2: Zoom Lens Attachment

Design 1: Threaded Cylinder

Overview: A clear (likely plastic) cylinder about 1’ in diameter that is internally threaded to allow the top to be rotated down using a small handle. The cell phone sits on the top so it can be rotated into focus. The scope is stationary at the bottom of the cylinder.

Figure 1: Basic Threaded Cylinder Housing Design

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Design 2: Zoom Lens Attachment

Overview: A table with a clear top for the cell phone to sit on. Below is a zoom lens focused onto the scope, sitting inside a clear housing. The user can manually operate the zoom lens to change the magnification on the cell phone screen.

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Schlieren Imaging System1) Optical Design2) First Order Analysis3) Test Plan 4) Risk Assessment

Optical Design Overview:

A point source will illuminate a spherical mirror and focus on a color filter that is 2x the focal distance from the mirror. An object that changes the density of the air around it (and in turn the index of refraction of the air) will be placed in front of the mirror and captured using a Nikon DSLR Camera.

Figure 1: Schematic of Optical Design

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Figure 2: Rough Drawing of Vision for Museum Exhibit

Test Plan / Validation1. Set up the optical design with all acquired parts for the system on optical table. Does the system

work?2. Shake the table and move the mirror. How far misaligned can the prototype be and still work?

This emulates excessive use by children.3. Insert different filters to see the effect they have on the end video output.4. Bring to RMSC Science Weekend and Test with children and families and receive their feedback

on filters, potential objects, and how to make the exhibit interactive.

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Risk Assessment The largest amount of risk as of now is injury. When dealing with a large mylar mirror, we have seen the potential damages that can occur when light is focused. With that in mind we must take all necessary precautions when working with the set up so that no one is harmed in the experimental process (especially the children)!

The second largest risk is optical alignment. It is not known yet how far misaligned the system can be and still function. With excessive use from day to day, we must access the prototype accordingly to assure it is robust enough for kids to play with over and over again and not misalign too much.

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References

[1] “Material Properties Tables – Acoustic Properties”. NDT Resource Center. < https://www.nde-ed.org/GeneralResources/MaterialProperties/UT/ut_matlprop_index.htm>

[2] “Closed-End Air Columns”. The Physics Classroom. < http://www.physicsclassroom.com/class/sound/Lesson-5/Closed-End-Air-Columns>

[3] “Open-End Air Columns”. The Physics Classroom. < http://www.physicsclassroom.com/class/sound/Lesson-5/Open-End-Air-Columns>

[4] “Refractive Index of Acrylic, Acrylate, Lucite, Perspex, Plexiglass”. Fimetrics. < http://www.filmetrics.com/refractive-index-database/Acrylic/Acrylate-Lucite-Perspex-Plexiglass>

[5] “50:50 Cube Beamsplitters”. Thorlabs. <https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=754>

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Documents

Design Description Document · Web viewA Rubens’ Tube design for use with water. Light scattering off of silica beads in the tube will help illustrate standing wave pattern. A subwoofer