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:
Engineers:
Advisor committee:
Calvin Uzelmeier (RMSC)
David Kim, Kara Morse, Madhu Ashok, Rebecca Pettenski
Wayne Knox, Joseph Choi
Document Number: 002
Date:
2/8/2016
Revision Level:
B
Authentication Block
This is a computer generated document and the electronic
master is the official revision. This paper copy is
authenticated for the following purpose only:
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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Contents
Product Requirement Document .................................................................................................................. 3
LED Rubens’ Tube ......................................................................................................................................... 3
Optical Design 1 ........................................................................................................................................ 3
Optical Design 2 ........................................................................................................................................ 4
First Order Analysis / Photon Budget ....................................................................................................... 5
Test Plan .................................................................................................................................................... 8
Risk Assessment ........................................................................................................................................ 9
Cloaking Device ........................................................................................................................................... 10
Cell Phone Magnification ............................................................................................................................ 23
Schlieren Imaging System ........................................................................................................................... 25
References .................................................................................................................................................. 28
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Product Requirement Document
(See digital document 001)
LED Rubens’ Tube
1)
2)
3)
4)
5)
Optical Design 1: Operation with smoke
Optical Design 2: Operation with water
First Order Analysis
Test Plan
Risk Assessment
Optical Design 1
Operation 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
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Optical Design 2
Operation 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 3
Operation 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.
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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):
𝑍2 − 𝑍1 2
𝑅=(
)
𝑍2 + 𝑍1
Material
Water
Acrylic
Resin
Aluminum
Steel
Air
Acoustic Impedance (g/
s*cm^2)
1.48E+05
Figure 3 – Table of Acoustic Impedance measured in (
3.15E+05
1.71E+06
4.54E+06
4.15E+04
𝒈
𝒄𝒎𝟐 ×𝒔
) for various materials [1].
Optical Design 1: Smoke
Smoke-Aluminum Interface
1.71𝐸+06 − 4.15𝐸+04 2
)
4.15𝐸+04
𝑅 = (1.71𝐸+06 +
𝑅 = 90.75%
Smoke-Steel Interface
𝑅 = 96.40%
Optical Design 2: Water
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Water-Aluminum Interface
𝑅 = 70.68%
Water-Steel Interface
𝑅 = 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].
𝑓1 =
𝑣
𝜆
𝑤ℎ𝑒𝑟𝑒 𝜆 = 4𝐿
𝑓1 =
𝑣
4𝐿
Given a fixed tube length with an open end, the wavelength corresponds to half of that in the closedend 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:
𝑣
𝑓1′ = 𝜆
𝑤ℎ𝑒𝑟𝑒 𝜆 = 2𝐿
𝑣
𝑓1′ = 2𝐿
Optical Design 1: Smoke
The 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)
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343
𝑓1𝑠 = 4∗.91 𝑓1𝑠 = 94.23 𝐻𝑧
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: Water
The 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.
𝑓1𝑤 =
1482
4∗.91
𝑓1𝑤 = 407.14 𝐻𝑧
Optical Design 3: Water Vapor
The 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.
343
𝑓1𝑤𝑣 = 2∗.91
𝑓1𝑤 = 188.46 𝐻𝑧
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∗𝐴
Where 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.
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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: Smoke
The 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: Water
The 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 watersilica bead interface.
(. 96)(. 997)(. 001)(. 997)(. 96) = .00092
Optical Design 3: Water Vapor
This 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:
𝐵𝑒𝑎𝑚 1: (. 448)(. 98)(. 98) = .4303
𝐵𝑒𝑎𝑚 2: (. 459)(.448)(. 98)(. 98) = .1975
𝐵𝑒𝑎𝑚 3: (. 459)(. 459)(. 98)(. 98)(. 98) = .1983
Test Plan
Optical 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 𝑓1 ≈ 120 𝐻𝑧
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.
Optical Design 2: Water
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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.
Optical Design 3: Water Vapor
1.
2.
3.
4.
Develop an optical system with 3+ parallel HeNe beams.
Create an isolated area for the spouts to decrease interference.
Develop a moving mirror to illustrate a profile of the output smoke.
Troubleshoot why frequency generator does not display high visibility.
Risk Assessment
Optical 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.
Optical Design 2: Water
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.
Optical Design 3: Water Vapor
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).
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Rochester Cloaking
1st Order Analysis
Focal Length and Thickness Requirements
Requirements
t1=(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 system
Object at infinity
Lens 1 and 2 act like Keplerian beam expander
Collimated light travels between lens 2 and 3
Lens 3 and 4 act like Keplerian beam expander
Image at infinity
Total magnification 1
Aperture (F/# & NA)
Entrance pupil is the objective lens
F/# =f/EPD
NA=nsinθ=nsin(0)=0
FOV
Entrance pupil is the objective lens
F/# =f/EPD
Wavelength Region
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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
Measure of object location with respect to lens.
Lens 1 conjugate factor = -1
Lens 2 conjugate factor = 1
Lens 3 conjugate factor = -1
Lens 4 conjugate factor = 1
G-Sums
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Minimize spherical and coma through minimizing bending factor (c1=c2). On a side note, Joseph Choi
reduces aberrations by using achromatic doublets.
Joseph Choi System
Source: http://www.opticsinfobase.org/oe/fulltext.cfm?uri=oe-22-24-29465&id=304785
Joseph Choi’s current system
Achromatic doublets
Lenses 1 & 4: 200mm focal length, 50mm diameter achromatic doublets BK7, SF2
Lenses 2 & 3: 75mm focal length, 50mm diameter achromatic doublets SF11, BAF11
Off 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 values
Spherical: 10.4
Coma: -8.6
Astigmatism: 8.2
Petzval: 0.4
Distortion: -8.4
7.7% for -1.5 degrees of field angle
Most aberrations occurred at the last two achromats
No optimization used except achromats.
Optimize radius of curvature & airspaces to start.
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Materials
Initial plan to optimize with custom lenses is not possible. Budget constraints dictate that we use offthe-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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23:46:46
Case
1
100.00
CloakSinglets
Scale:
0.25
DK
MM
03-Mar-15
Object angle ranges from ±0.75 degrees.
Case 2
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22:43:21
119.05
CloakSinglets
Scale:
0.21
DK
MM
03-Mar-15
Object angle ranges from ±0.75 degrees.
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22:48:27
Case
3
125.00
CloakSinglets
Scale:
0.20
DK
MM
03-Mar-15
Object angle ranges from ±0.75 degrees.
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23:52:43
Case
4
100.00
CloakSinglets
Scale:
0.25
DK
MM
03-Mar-15
Object angle changed to ±0.3 degrees.
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00:48:06
Case
5
125.00
CloakSinglets
Scale:
0.20
DK
MM
04-Mar-15
Object angle ranges from ±0.3 degrees.
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00:12:50
Case
6
125.00
CloakSinglets
Scale:
0.20
DK
MM
04-Mar-15
Object angle ranges from ±0.3 degrees.
Edge rays deviate from ideal path too much. Need to reduce object angle. This makes this case
impractical.
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00:55:41
Case
7
138.89
CloakSinglets
Scale:
0.18
DK
MM
04-Mar-15
Object angle ranges from ±0.3 degrees.
Edge rays deviate from ideal path too much. Need to reduce object angle. Design may be impractical
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01:07:35
Case
8
125.00
Test
Scale:
0.20
DK
MM
04-Mar-15
Object angle ranges from ±1.5 degrees.
Conclusion
Referring 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 Magnification
1) Design 1: Threaded Cylinder
2) 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 System
1)
2)
3)
4)
Optical Design
First Order Analysis
Test Plan
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 / Validation
1. 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.ndeed.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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