Holography Lab

Experimental caveats:1. Always take care when working with the laser as it can seriously injure your eyes.

Don’t look directly at the laser, and try to keep the beam path in mind when moving around the lab. Remember to keep the laser off when it is not in use.

2. Place the Ziploc bags over the optics components each day when you are finished; dust can ruin your holograms.

3. The chemicals in the darkroom can irritate your hands and are dangerous for your eyes. Always handle with gloves and goggles and tongs.

4. If you use the laser beam profiler, make sure to keep the fixed attenuator IN, to avoid oversaturating the detector. Take care not to get dirt/dust in the camera. Do NOT drop the $5,000 camera!

Data to take:1. Use a Michelson interferometer setup to test the stability of the optics table and to

determine a coherence length for the laser.2. Create a set of holograms to test your set up and develop them.

Points to ponder: 1. How can holography be used in physics applications?2. Can holograms be made without the use of a controlled, laboratory-like environment?

Other things to explore:1. White Light Holography, a technique where the reference beam shines in on the other

side of the hologram so that normal white light can recreate the hologram.2. Pseudocolor Holography, where two or more differently colored lasers are used to

expose the film, allowing for the creation of holograms with color.

HOLOGRAPHY

I. IntroductionHolography is a powerful imaging technique that allows you to store and recreate a wavefront. As a result, you can create an image that is fully three dimensional, just as if you were looking at the original image. This can be more than just an artistic curiosity, as holography has been used for data storage, diffraction gratings, security tags, and archival recordings of three-dimensional objects -- essentially most applications in which a 3-D image reconstruction is of value.

II. ObjectivesThe principal objective of this lab is to become familiar with the process of creating holographic images and gain experience working with optical equipment. In the course of the exercise, you will create a Michelson Interferometer to measure the sensitivity of the equipment to vibration and the features of the laser. You will learn how to tune and position spatial filters. Once fully acquainted with the equipment, you will create a series of holograms and finally process them in a darkroom.

III. Preparation

Read the reference materials in this manual to gain some understanding of holography -- pay particular attention to the selections from the optical holography book. Below, we will outline some of the main features.

As mentioned above, holography is the process of capturing an image of a three dimensional object on film. This could equally well be a description of photography, so it is important to understand the differences. In photography, you capture only the amplitude information of the incident light by recording the intensity of light, which is proportional to the amplitude squared. Relative phase information is lost, and the scene then is not perceived as three-dimensional. In holography, you record intensity of light again, but make use of the phenomena of interference. The intensity is now that resulting from the incident light relative to a reference light and in that way, you have recorded both amplitude and phase information about the incident light, thus retaining all the information about the scene. The hologram records the whole incident wavefront,

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preserving parallax and allowing the viewer to look around the edge of objects, just as they could with the original scene.

It is relatively simple in theory to consider some basic aspects of this process. Take a coherent, monochromatic source of radiation (i.e. a laser) and shine it off an object. The light scattered from the object, the source beam, is incident on the film, and upon reaching the film interferes with a coherent beam of radiation, the reference beam. Recall that a maximum in amplitude of interference is created when the waves from the object and reference are in phase, and a minimum in amplitude of interference is created when the two are 1800 out of phase. Thus, an interference pattern is created on the film.

To extract phase and amplitude information about the object from the interference pattern is remarkably simple. Simply shine the reference beam back through the exposed film, and the diffraction effects from the interference pattern in the film will recreate the original scene.

To illustrate this more concretely, let us briefly examine the idealized case of a point source as our scattering object. Let the reference beam be incident perpendicular to the film. Place a point source, O, in the beam’s path, as in figure 1. The light will scatter off of O in spherical wave fronts, which will be incident on the film as shown in 1. These two wave fronts will create a circular interference pattern on the film, depending on the phase difference between the waves (the analysis of this is very similar to that of a two slit interference pattern, which can be found in any introductory textbook).

When the film is placed back into the reference beam, without the object, diffraction effects from the interference pattern on the film reinforce the reference beam so that the beam seems to be diverging from the point O’ (figure 2). Looking through the hologram towards O’ and you would ‘see’ O (for all intents and purposes, the light appears to be diverging from O). Note that O’ isn’t actually a real image: it is virtual, (just like the image you see of yourself in a mirror). There is a symmetric point of conversion on the other side of the film as well, labeled I which is a real image that you could focus on a screen, although in practice, as discussed later, it is not observed.

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Taken from Intro to Optics, by F.L. Pedrotti and L.S. Pedrotti, Prentice Hall, 1993.

Now let us look at the much more interesting case of extended objects. From the discussion of a point source above, it is obvious that the reference beam and the real image would interfere with viewing the virtual image created by the hologram. This problem can be solved by the method of off-axis holography, as described below.

A setup that can be used for off-axis holography is shown in figure 3, where Er is the reference beam, Es is the subject beam, BS is the beam splitter, and M1 and M2 are mirrors one and two. The source, a He-Ne laser, is split by the beam splitter, from where it diverges to mirrors one and the object. Mirror one reflects the beam onto mirror two, and from there onto the film at an angle α to the film normal, as shown in figure 4. This is the reference beam. The undeflected beam from the BS is incident on the subject, from where it scatters diffusely onto the film which lies in the x-y plane.

Let the electric field of the reference beam at the film be represented by equation 1:)( φω += ti

r reE

4

(1)

Figures 3 and 4. 3 – A possible off axis holography setup. 4 – The incident reference beam on the film. Ibid.

The amplitude r=r(x,y) can be assumed to be constant, as the reference beam is a plane wave. φ is a phase angle, which arises from the angle, α, between the reference beam and the film normal. Letting the top edge of the field strike the film at x=0, φ becomes a linear function of distance, x along the film plane, as described in equation 2.

€

φ=2πλ

∆=2π

λ

xsinα

Let the subject beam be the field in equation 3.)( θω += ti

s seE

where s=s(x,y) is the amplitude function of the scattered light, and θ=θ(x,y) is a complicated function representing the phase shift of the light scattered from the object. Note that were only the subject beam illuminating the film, the irradiance or intensity, If, experienced by the film (what the film grain responds to) would simply be as equation 4, where β is a constant.

22),( yxsEI sf ββ ==

This contains only amplitude information and no phase information.

However, if we illuminate the film with a reference beam, then the total field at the film is as equation 5, and the irradiance experienced by the film is as equation 6.

srf EEE +=2

ff EI β=

( )( )srsrf EEEEI ++= **β

( )rssrf EEEEsrI **22 +++= βThe irradiance function now contains the function θ, which is the phase information; explicitly, equation 7 shows the irradiance experienced by the film.

( ) ( ) ( ) ( )( )θωφωθωφωβ +−+++− +++= titititif erseersesrI 22

( ) ( )( )φθφθβ −−− +++= iif rsersesrI 22

When the film is developed, its transmittance, t(x,y), is directly proportional to the irradiance. To view the hologram, we re-illuminate the hologram with the reference beam, equation 1. The emergent beam can be expressed as in equation 8, where κ is another constant.

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Eh=tEr=reiωt+φ( )κr2+s2( )+rseiθ−φ( )+rse−iθ−φ( )[ ]

This gives rise to several different terms. The first term, called the zeroth-order diffraction, is as equation 9. It simply is an amplitude modulated version of the reference beam.

( ) )(221

φωκ ++= tih esrrE

The second term, equation 10, is an amplitude modulated reconstruction of the original subject wavefront. It contains all the original information, and appears to be diverging from the original object. This is what creates the virtual image that we usually refer to as the hologram.

)(22

θωκ += tih serE

The third term, equation 11, is an amplitude modulated version of the subject beam that has a negative phase from what it had before. In addition, the phase has been shifted by

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(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

2φ. The effect of this phase reversal is to cause the beam to converge towards the point of the original object, shifted by an angle of 2α out of the path of Eh2. This creates a real image. Figure 5 illustrates the three emergent beams.

)2(23

φθωκ +−= tih serE

In the above discussion, we have neglected the thickness of the actual hologram and assumed in the reconstruction that the holographic plate is thin enough so that no additional effects occur upon transmission of the light through it. In practice, our film is on the order of 20 wavelengths thick, so rather than a plane hologram, we actually record a volume hologram. As described in the article by Toal in Am. J. Phys., this adds additional complications to the analysis. Practically speaking, it also means that the first order real image is not observed.

IV. Equipment List

Holography Room:1. He-Ne 10 mW laser2. Beamsplitter3. Edmund Optics mirror x24. Edmund Optics spatial filter, holder and microscope objective x25. Film holder6. Optics table7. (Optional) Coherent BeamView 4.4.0 Laser Camera with C-VARM (continuous

variable attenuator module)8. Lamp and safelight and flashlight

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Figure 5 – Emergent beams upon placing the hologram in the reference beam. Ibid.

9. Ruler and meter stick and level10. Shutter mechanism, includes shutter, controller and two power supplies labeled 1

and 211. Holographic film and light tight envelope for carrying exposed film12. Scissors

Darkroom:1. Chemicals: Developer A&B, Bleach [provided by instructor]2. Developer Trays x53. Safelight4. Rubber tubing x25. Gloves6. Goggles7. Tongs8. Drying Rack9. Timer10. Plastic Squeegee

V. Procedure1. Michelson Interferometer

Before getting started with holography, you should understand the limitations of our experimental setup. Much like photography, changing the position of the light incident on our hologram mid-exposure will certainly distort the hologram. Thus, you should assess how sensitive our setup is to vibrations. It is also important to understand the limitations of our light source, in particular the coherence length of the laser. If the light is no longer coherent, then we certainly can not store phase information anymore! Look at the readings from Collier and Smith for a more complete sense of what is meant by coherence.

The easiest way to get a sense for how sensitive our system is to outside disturbances is to make a Michelson Interferometer. From 212 lab or the Michelson lab, you should be familiar with the basic idea. (Review the Michelson lab handouts, if you are not.) If you take a coherent beam, split it, send the two components along different path lengths, and then recombine them, you will get an interference pattern due to the phase shifts of the split beams. This setup is extremely sensitive to small changes (that cause the path lengths to change, and the interference pattern to shift from light to dark or vice versa). As a result, a Michelson interferometer is a good way to qualitatively assess how sensitive our system is to disturbances in the environment. The presence or absence of an interference pattern can be used to determine the laser coherence length as well.

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Setup

1. If not in place, place the beam splitter in the path of the laser beam, close to the source. Note that our beam splitter doesn’t do the typical 90° split of the standard Michelson Interferometer, so we’ll be working at odd angles.

2. Place the mirrors so that the beams from the beamsplitter land on the mirrors. Adjust the position of the mirror that is in line with the laser beam to make sure the path length between the beam splitter and each of the mirrors is roughly equal.

3. Adjust the mirrors so that all laser spots align. The easiest way to do this is to notice that you should have three spots all going back to the laser cavity, which should all align on the exit point of the laser if the mirrors are positioned correctly.

4. Observe the interference pattern created on the wall. Place a piece of white paper there to see the pattern more clearly. Try walking around, talking, coughing, etc. How sensitive is the pattern to disturbance? Record your observations.

5. Determine an estimate for the coherence length of the laser by adjusting the mirror that is in line with the laser beam. For what path length difference is the interference pattern no longer noticeable? What is your estimate of the degree of uncertainty in your measurement?

In doing steps 4 and 5, you may find that you have an additional issue--actually three beams interfering (the two split by the beamsplitter and back from the mirrors + reflections from the laser cavity itself). You can see the issue more clearly and work around by using the laser beam profiler used in the laser lab. To operate the camera, you should read the separate instructions for the camera. Make sure to keep the fixed attenuator IN, so as to not saturate the detector. You should be able to see the interference fringes as well as how the various beams are converging. Be sure to put the lens cap back on when you are done. [If we were actually interested in the interferometer, we could have either expanded the beam as is done in the Michelson Interferometry experiment or gotten a wedge to offset the beams....]

2. Tuning the Spatial Filters

It is necessary to reduce spatial noise in the beam as much as possible, so as to get the clearest possible hologram. The spatial filters do so in a manner described in the appended section, A Note On Spatial Filters. Read the information and adjust the filter nearest to the straight through beam mirror. The other spatial filter should be reasonably well aligned, although you will probably need to adjust both for your hologram.

3. Imaging the Hologram.

To make your hologram, pick an object (or objects) to image, although it is recommended to choose something fairly reflective, and possibly involving a magnifying glass, as that

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demonstrates the holographic effect well. Note that all of the beams should be level; use the clear plastic ruler to confirm this as you go through each step of the procedure.

Setup

1. Make sure the beamsplitter is in front of the laser and a mirror is further down the original path of the laser. Reflect the beam across the optics table onto an object. The object should be near to the object mark on the table, but need not be exactly on it. Place the film holder so the object is directly on axis with it.

2. Measure the path length using the string and a meter stick available for this purpose. While adjusting the beam splitter angle as necessary, direct the split beam to the second mirror, and from the second mirror to the film holder. This is the reference beam, and should be incident at an angle to the film holder. Measure this path length, and make sure the difference in the path lengths is no more than the coherence length of the laser you have already determined.

3. Align the spatial filters after the mirrors, and go through the necessary tuning procedure until you have the most diffraction free beam you can achieve for each.

4. Put the shutter in between the laser and the beam splitter, making sure the beam is going directly through the shutter aperture. Learn how to operate the shutter. You must turn on the power supplies in numerical order (1 then 2), and off in reverse order. The power supplies are set to their proper voltages (1 is at 5 V, 2 is at 25 V), so do not adjust them. The time on the timer is in seconds (4.00 = 4s). You must reset the shutter every time before opening it, especially if you change the time. The time change won’t happen if you don’t reset before opening the shutter. [We are in the process of building a new shutter that’s more intuitive!]

5. Use the portable light meter to measure the intensity of the reference and object beams (separately) at the film holder. The ratio of their intensities should be somewhere between 3:1 to 10:1 reference to object, with 4:1 being an ideal intensity ratio. You will want all the lights off in order to reduce background. If your ratio is not in this range, double check your spatial filter tuning, and talk to the instructor.

6. With all the lights off except the safe light and laser, check the scattered light as well, making sure that you have only the desired interference in your hologram. Use the pieces of black felt and black construction paper to place light barriers in such a way that you eliminate the possibility of extra scattering from most of this scattered light.

Taking the Image

Before making a final image, you need to figure out what a proper exposure time is. This is around two minutes, but will vary depending on the object chosen and the ratio of

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intensities of reference beam to object beam. You should also finish reading this procedure, and the darkroom procedure, and spend some time familiarizing yourself with the darkroom and mixing chemicals, so that you are ready to develop the film you image on. Before starting to take the image, make sure that you have located your light tight envelope within which you will carry the film to the darkroom.

1. To avoid wasting film, while doing test runs you should not use whole pieces of film, but rather quarter pieces. When you are ready to make your first test run, turn off all the lights except the safe light and the laser, and make sure the shutter is closed.

2. Remove a piece of film from the film bag, and then store away the rest of the film in its light tight bag. Cut the film into quarters. Mark each quarter so you can identify it (an easy way to do this is to cut a tiny bit out of the corner of each one, in different shapes).

3. Place one of the pieces of film into the film holder, centered in the reference beam. Shield the rest of the film (put it in a light tight bag).

4. Set the timer for your chosen time (it is recommended that you do a range of times around 2 minutes with your four test pieces. For example: 40s, 80s, 120s, 160s). Note that if you need to do exposures longer than 99s, you will need to do a double exposure (two 60s exposures for a 120s exposure). [This procedure should simplify with the new shutter.]

5. Open the shutter and expose the film. 6. Place the exposed film into the light tight carry envelope. Expose the other test pieces. Develop them, after speaking with your instructor before going to the darkroom. Read the appendix on dark room procedures.

7. If you’re getting diffraction effects in the hologram, check to make sure that stray light isn’t getting onto the film, that you’ve eliminated diffraction effects from the spatial filters, and that your film is centered in the film holder.

8. Once you have determined the proper exposure time and eliminated diffraction effects, take a final image on a ½ a piece or a full piece, depending on how much film you’ve used up to this point. (Consult your instructor before doing so.)

VI. Reporting Your Results

1. Describe the results of your interferometry setup--what level of vibration or disturbance would result in changes in the interference pattern observed? Be as quantitative as you can. What is your estimate for the coherence length of the laser? What do you think sets the value of this?

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2. Describe your final hologram and the steps you took to insure its success. If you did not get a 3-D image, discuss possible sources for your difficulties. Answer in particular, why is there a limited ratio of intensity of the reference beam to the object beam in which the hologram will expose properly?

3. What was your exposure time for your hologram? What happens (qualitatively) if you over or under expose your hologram? What happens in the developing process to give you a final hologram? Consult other resources as necessary to determine the role of the chemicals you have used. (The internet in particular can be useful for this.)

4. Discuss the differences between an amplitude and phase hologram, a plane or a volume hologram, and a reflection or transmission hologram. What type of hologram did you make? What would be necessary to make the other types?

5. Describe in some detail the potential application of holography to one of the following areas: interferometry, data storage, microscopy. Locate and attach a recent (last five years) reference in one of these areas, explaining how the particular article you have chosen uses holography.

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A Note on Spatial Filters

Inevitably, a laser beam suffers from spatial aberrations as a result of scattering off dust on lenses or mirrors or imperfections in the optical equipment. Yet, making a hologram requires a spatially coherent monochromatic source of illumination. A spatial filter is a piece of optical equipment that removes spatial aberrations to obtain a cleaner beam.

It can be shown that if we shine a diverging beam of light through a lens, the resulting light at the lens’ focal length is a Fourier transform of the incoming wave. If we then place a pinhole directly at the center of the lens’ focal plane, the transmitted wave is only the base part of the Fourier transform, the lowest frequency wave, without any of the higher frequency oscillations.

A spatial filter is a clever device that allows us to do just this. By putting a small aperture in the focal plane of a microscope objective, we are able to achieve this filtering effect, and get a pure plane wave diverging from the aperture. The necessary size of the aperture depends on the size of the spot produced by the lens at its focus. This spot’s size depends on the wavelength of the laser, the beam waist of the incident beam and the focal distance of the lens as listed below from the Edmunds website.

Beam Spot Diameter (microns) = (1.27 * λ * f) / D where, λ = wavelength of laser (microns) f = focal length of objective lens (mm) D = input beam diameter (mm)Pinhole size is then determined for Pinhole Diameter (microns) = 1.5 * Beam Spot Size Diameter (microns)where the factor of 1.5 is determined as the optimal factor in order to pass the maximum amount of energy, while eliminating as much spatial noise as possible.

Setting up the Spatial Filter

1. Examine one of the spatial filters by unscrewing the pinhole and unscrewing the microscope objective. It is preferable to work on the assembly closer to the undiverted laser beam.

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http://www.edmundoptics.com/techsupport/DisplayArticle.cfm?articleid=272

2. Replace all the parts except the pinhole and secure the filter to the optics table so that the laser beam passes into the open end. Use the fine adjustment base screws to center the laser as best you can in the lens.

3. Place a sheet of paper in the path of the light coming out of the objective. Note that the beam contains various disruptions, diffraction patterns, spots, etc. This is interference from imperfections in the lens, dust, etc. Screw the micrometer drive on the back of the instrument to 1mm.

4. Put the pinhole back into its slot and if you haven’t already done so, turn out the lights for better viewing. You may switch on the power strip on the table to turn on the safelight and table lamp or use a flashlight. You should see faint dots on the paper. If not, use the fine adjustment screws to visually maximize the light coming through the pinhole (visible by looking at the back of the pinhole).

5. Play with the pinhole fine adjustment screws until the dots begin to align. As they get closer the dots should brighten and a bright circular diffraction pattern should appear on the sheet.

6. Using the bottom plate screws and the clear ruler provided, ensure that the beam leaving the filter stays level at about 12 cm.

Tuning the Spatial Filters

1. Put the spatial filter down in the path of the beam and adjust it as described in the set up procedure above.

2. Place a piece of paper in front of the spatial filter at a distance of 10-15cm, so as to be able to clearly see the output beam of the spatial filter.

3. Screw the microscope objective in to the minimum range on the micrometer screw drive.

4. Adjust the pinhole screws so that you get a maximum brightness. This should result in a circular diffraction pattern, as in figure A1.

5. Adjust the height and angle of the spatial filter for maximum brightness.

6. Begin driving the screw away from the pinhole, note that the diffraction pattern moves and changes in intensity. This is because the micrometer screw drive isn’t perfectly level, so the height of the incident beam changes as the screw is driven.

7. Continue to move the objective back, adjusting the pinhole position as necessary to maintain a bright interference pattern.

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8. At some point (around 2mm out) the interference should change from a circular aperture diffraction pattern to a pattern visually similar to a double slit diffraction pattern (what might cause this?), as in figure A2. Adjust the pinhole screws and micrometer drive until this resolves into a single spot, as in figure A3.

9. Fine tune the pinhole adjustments and the objective distance to achieve the best spot you can (no diffraction patterns. Turn out the lights to see if there are any faint rings!). You are looking for maximum brightness and, more importantly, no diffraction.

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Figure A1 – A circular diffraction pattern from the spatial filter.

Figure A2 – The visual double slit effect.

Figure A3 – A diffraction free spot.

Darkroom procedures

Before you begin, it is important to note a few things. First, the darkroom belongs to the Biology Department; please treat it with respect and care. Second, the only light that is safe to use around our film is the green safe light marked ‘physics department’ on it. Any other light in the room, including the traditional safelights, will expose the film. The film is not light safe until after it has been bleached. Third, examine the various faucets provided in the sink, the blue and red are normal tap water, while the white faucets are high pressure De-Ionized water, generally referred to as DI.

Also, all of the chemicals used in this lab, particularly the bleach, are dangerous to skin contact. Wear goggles and rubber gloves and use the provided tongs to handle the film in the developer and bleach. If you get chemicals on your skin, then immediately wash affected area thoroughly with water. Read the Materials Safety Data Sheets associated with the chemicals so you have some idea of their toxicity. Consult the instructor if you have any questions.

The chemicals should be provided by your instructor. Make sure that you have Developer A, Developer B, and Bleach on hand. If not, talk to your instructor. You may need to mix the chemicals. If this is the case, follow the instructions appended in the Mixing Chemicals section. Please dispose of the chemicals in the waste bottles provided.

Setting up the Darkroom

1. Position the safelight so it illuminates the entire sink area.

2. Place your five trays as follows: small, large, small, large, large. Order left to right or right to left as you see fit. These trays will become your developer, rinse 1, bleach, rinse 2, and rinse 3 trays respectively.

3. Wash all trays with DI and soap (particularly important for the first use. After that, a rinse with DI water is sufficient).

4. Set up the rinses. Fill the rinse 3 tray with 1.2L of DI water, and then add a capful of a chemical known as photoflo. Fill the rinse 1&2 trays with DI water. Attach one of the rubber hoses to the DI tap, and run it into one of the rinses. Leave the water on, so there is a constant influx of DI water into the rinse (you may need to clip the tube to the side of the tray, a clothes pin works well for this). Repeat with the other hose and rinse. Turn the DI on.

5. Add 100mL of Developer A and 100mL of Developer B to your developer tray (the first small tray in your sequence). Agitate by gently rocking the tray from side to side to mix.

6. Add 200mL of Bleach to your bleach tray.

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Developing

1. Quickly submerge the entire film in your developer mixture. Agitate as described above for two minutes. The hologram should turn black.

2. Remove the hologram from the developer (use tongs!) and place it in Rinse 1. Let it rinse for three minutes.

3. Place rinsed hologram in the bleach. Agitate the bleach until the hologram turns clear (this should take no more than two minutes).

4. Remove it from the bleach (use tongs!) and place it in Rinse 2. Again, let it rinse for three minutes.

5. Remove it from Rinse 2 and place it in Rinse 3. Rinse for 40s.

6. Remove from Rinse 3 and place on drying rack (a paper towel on the counter will do).

7. Use the squeegee to gently remove excess water from the film.

8. Allow it to dry completely.

Consult your instructor or the lab assistant about proper disposal of the chemicals.

Mixing Chemicals

Be sure to first clean all equipment with DI water and the provided soap. For each solution, fill an appropriately-sized bottle with warm DI water, add the chemicals and dissolve one by one. Order doesn’t matter. Scale as appropriate (ask instructor).

Developer A:20g Catechol10g Ascorbic Acid10g Sodium Sulfite75g Urea1L Distilled Water

Developer B:60g Sodium Carbonate, Anhyd.1L Distilled Water

Bleach Solution:

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5g Potassium Dichromate80g Sodium Bisulfate1L Distilled water.

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