Thanks for taking the time to look at the CorticalCafe CGHMaker otherwise known as The Computer Generated Hologram Construction Kit.  With this program and some simple office supplies, you can make your own holograms without even using a laser! 

This page has some background information and describes the Cortical Cafe CGH program functionality, and there are complementary step-by-step instructions here.

What is a hologram?
A hologram is a snapshot of "wave-fronts" from a scene.  The hologram records information so that it may be reconstructed in three-dimensions, whereas a photograph merely records a two-dimensional projection of the scene.  Certain limitations apply to creating and viewing holograms.  In particular:

• Special light - Because holograms depend on constructive and destructive interference of light waves to recreate the scene in three-dimensions, light from a laser is usually required in some capacity.  Laser light is special because it is "coherent" temporally and spatially.  This means that all light waves from a laser have the same "phase", the same "frequency", and usually the beam remains almost perfectly parallel (doesn't diverge or converge).  You don't always need a laser to view a hologram (though that will give the cleanest reconstruction), but usually a monochromatic (single color) point source of illumination works best.
• Motionless environment - Because the light wave interference must be recorded on film, it is essential that nothing move, or else the recording will blur and become useless.  The physics of holography stipulate that motion must not exceed 1/4 of the wavelength of recording light, or about 160 nm (nanometers).  Air currents, sounds, and even expansion of materials due to temperature changes all have potential to prevent image recording.
  

• Transmission hologram - This hologram is viewed by placing a light source behind the hologram and looking through it (like a window).  The hologram is recorded in a two-dimensional format on the film plate. 
• Reflection hologram - This hologram is viewed by looking at the reflection of a light source in the hologram (like a mirror).  This type of hologram depends on the holographic fringes being recorded in three-dimensions (Bragg refection) on the film plate.

• The information in a hologram is distributed - if you cut it into pieces, you will find that each piece contains enough information to reconstruct the entire scene.
• Image projection - under some circumstances, merely shining a laser through the hologram projects an image on to a screen.  No lenses, no optics, nada.
• Viewing directly with a point source - Using a point source of illumination, a hologram reconstruction presents the exact same light wavefronts to your eyes that they would receive with the real object.  The hologram is indistinguishable from the physical object. 

• Use a simple list of points (like pixels, except we call them voxels because they are points in three-dimensional space) - Using this method, you can create a hologram of something simple, like a cube, or a square.  The points are defined in XML using a very simple syntax and may be edited in almost any text editor.  This is the simplest way to define a 3 dimensional object.
• Create a 2 dimensional GIF image and turn it into a hologram - Using this method you can turn a word or a picture into a hologram using a simple paint program.  White pixels are considered "background" while black pixels are considered "points" in the object.  This is the simplest way to define a 2 dimensional object.  I suggest starting with very small (eg, 10x10) images.
  
• Create your hologram programmatically using the Java programming language-  This method will allow you to create objects which are as complex as you desire.  You don't need to be a hard-core programmer to use this method and you do not need external tools like compilers, development environments or anything else other than a simple text editor.  This is the most complicated method of defining an object but gives you complete control over what your reconstructed image should look like.
  

Sample files demonstrate all three input methods. 

What does the computer generated hologram output look like?

The hologram output is the fringe pattern of intensity variations that are recorded on the holography plate.  Normally these would be recorded as the constructive and destructive interference of wavefronts from reference and object beams at the photographic plate.  Since this is a simulation, your output will be a JPG image containing some representation of the wavefronts.  If you look at the edge of the CGH pattern, you will see that it varies black-white-black-etc. with almost every pixel. This means that the hologram is using maximal output bandwidth. Moving the object off axis any further will violate nyquist sampling on the output and cause distortions (ie, aliasing).

Fresnel Zone Plates... what fun! The image on the left is the interference pattern that occurs between a single point source and a plane-wave at the photographic plate. Use this file if you want to calculate the lens yourself. Since this is essentially a Fresnel lens (though real lenses usually modulate phase by varying refractive index or lens thickness), we see a series of cencentric rings with varied spacings around the center of the image. The image on the right demonstrates the quantization artifacts which occur because of the binary output of the printer. The multiple smaller circles located symmetrically around the plate will degrade lens performance.

What does the reconstruction look like?

The reconstruction from an image with the letters "AB" is shown here.  The bright spot in the center is the "DC component", the undiffracted laser beam.  Diffraction from the computed fringes produces a reconstructed image which can, to an extent, be moved away from the unmodulated beam.  Unfortunately, the modulation produces a similar image with axial symmetry on the other side of the DC spot, though this could be eliminated with spatial filtering.  Much of laser beam is used to produce artifact instead of contributing to the image reconstruction, suggesting low efficiency for the technique.  A number of inaccuracies exist, mostly related to the output of the fringes.  But stop complaining... it works! By the way, he reconstruction you see here is created simply by shining a laser-pointer through the hologram. If you use some simple optics to illuminate a larger part of the hologram or even a poorly collimated laser it should increase the signal/noise ratio of the reconstruction.

Here is a photo demonstrating the reconstruction setup.  It is simply a laser pointer beam aimed through the computed fringes which were printed on a transparency.  Since the collimated beam from a laser pointer is still a few square millimeters, it covers hundreds of plate pixels and can reconstruct an intelligible image. Note the ping-pong paddle/box mount holding the transparency.  Similar scientific apparatus may be purchased at a local sporting retailer if necessary.

The CorticalCafe CGHMaker software interface

• Plate controls
• x/y resolution - the number of pixels on the plate
• x/y sampling - the spacing between pixel centers on the plate in meters (see spatial sampling rates below)
• x/y offsets - the offset in meters of the plate from the normal axis of the object beam
• 1 inch QuickPick - this is a quick way to set the program to compute a 1-inch hologram at the most common printer resolutions.  For example, if your printer is 600DPI, then choose 600x600 and the resolution and sampling fields will automatically be chosen.
  
• Misc controls
• Center plate - centers the object with respect to the X/Y axis of the plate.
  
• Randomize Phase - apply random phases across the object, reduces speckle artifact caused by coherent interaction between light rays from the object.
• Diffraction grating - if checked, will produce a diffraction grating instead of a hologram.  Useful to test the resolution of the output device
• Diffraction grating multiple - if diffraction grating is selected, this is related to the order of the grating.  Use "1" for finest fringes to test the resolution of the output device.
• Object controls
• Depth - defines how far (in meters) along the Z axis an object will be focused from the plate during reconstruction.  For example, if the plate will be 10 feet away, enter 3.05 (305cm) into this field.
  
• Opt Depth - checking this box will compute and use the minimum depth that is possible without exceeding the resolution of your output device (aka, aliasing).   Uncheck this box if you want to control the focal distance manually or you have a 3 dimensional object (eg, a JAVA or XML input file).
  
• Center - checking this box centers the object along the normal axis to the hologram plate.  You will almost always want this to occur.
• Scale - checking this box scales the object to the same size as the hologram plate, ignoring the GIF sampling field.
  
• Sampling - If an image file is used as the object, this defines the spacing (in meters) along the X/Y axes of the object. For example, if your image is 10x10 pixels and spacing is 1e-3, then your image will be 1cm high.
  
• Wavelength - defines the wavelength of light (in meters) used to create the hologram in meters.  A value of 630e-9 is typical for a "red" Helium-Neon (HeNe) laser and close enough to inexpensive diode-laser pointers (usually 635-658nm).
• Input file - this field defines the input for the hologram, and may be a GIF, JAVA or XML file.
  
• Start/Stop computation - Starts computation of the hologram.  Processing may take many minutes for a large complex simulation.  Progress is displayed in the status display along with an estimate of the total time required.  Once the hologram is computed, you may display the output as many times as you wish using different output algorithms without recomputing.  Pressing this button during a computation aborts processing.
  
• Display output selection - Selects how to display the output.  Since most output methods are binary (eg,  laser and inkjet printers are essentially black and white and can not really display shades of gray),  a "binary" output is most appropriate for printing.  Sometimes, however, it is fun to see the full gray-scale of the fringes on a monitor.  You can work through the math to understand the difference between looking at phase, amplitude,real, or imaginary channels, and these are present for you to examine.  But when you print your hologram, quantization and sideband artifacts will invariably be present regardless of what output method you choose.  I suggest you use the real channel with binary output for printing.  BTW, holography film doesn't record amplitude at all, it records intensity or power, the square of amplitude.  And in a nonlinear fashion, at that.
• Display output - displays the computed hologram according to the selected display method.  Note that you can display the hologram multiple times using several different display types without recomputing anything;  just change the display output selection and press the "Display output" button.
  
• Misc Menu
• Normalize output values - This scales output values so they don't exceed limits of the numerical types used in the simulation and for output.
• Use Threading - The code will use all available CPU processors in your system unless you uncheck this box.
• Low priority - This helps manage CPU load with respect to other tasks on your computer.
• Use attenuation - This reduces simulation energy based on the distance between points in the object and plate.
  

Examples

Example 1:  Create a diffraction grating
A diffraction grating is a series of closely spaced lines which diffract or "bend" light passing through them.  Creating a diffraction grating is a good way to test the resolution of your output device.  Create a diffraction grating as follows:

1. Selecting "diffraction grating" on the interface, select the order as '1'
2. Select a plate resolution.  If your laser printer is 600x600DPI, then select that resolution.
3. Press "Start computation" to start, the status bar will indicate when the computations are finished (almost instantaneous on my low-end machine).
4. Select "Real_Binary" output and press "Display output" to display the grating.
5. Select "File" and "Save" from the menu on the fringes.  Enter a name (eg, diffgrate_01.gif) to save it.
6. Load the hologram with another program.  Send to a printer and print at the highest resolution (eg, 600x600 DPI).
7. Test your grating by shining a laser through the slits.  By measuring the distance between the hologram and the projections screen, and the distance between the undiffracted beam and the first diffraction lines (m=1 in this case), you can determine the angle, , which the light has spread.   If you are using a red laser, then is approximately 630nm (630 * 10^-9 meters).  Plug your numbers into the diffraction equation (d=m*/sin()) to confirm the resolution of your printer.
   

1. Make sure that the "Diffraction Grating" is unchecked, otherwise relevant options will be disabled.
2. Select plate size and resolution.  Since we're using a 600 DPI (dots per inch) laser printer, let's choose a 1 square-inch hologram by selecting the plate as 600x600 pixels with 423e-7 m spacing.
3. Select the "letterA.gif" image, depth 2 meters, scale object (this sets the sampling to approximately 6768e-7 and will make the object about the same dimension as the plate), wavelength 630e-9.
4. Select randomize phase to eliminate object-object coherent noise (speckle) in the simulation.
5. Press "Start computation" to start.
6. Follow the progress in the status bar, when the hologram is 100% completed computation will stop. Total computations take about 2-minutes on my low-end machine.
7. Select "Real_Binary" output and press "Display output" to display the hologram fringes.
8. Select "File" and "Save" from the menu on the hologram.  Enter a name (eg, letterA_RealBin_01.gif) to save it.
9. Load the hologram with another program.  Send to a printer and print at the highest resolution (eg, 600x600 DPI).  See printing notes below.
10. Look through the hologram when illuminating with a tiny but bright non-laser light source or project the image onto a wall by shining a laser-pointer through the hologram. 
11. At this point you can also change the output to other options (eg, Imaginary, Phase, etc.) and press "Display output" to see what other representations of the complex-valued result look like.  The hologram does not need to be recalculated to see alternate outputs.

1. Select plate size and resolution.  Since we're using a 600 DPI (dots per inch) laser printer, we will select the plate as 600x600 pixels with 423e-7 m spacing.
2. Select randomize phase, "Center plate" should not be checked
3. Select the cgh_cube.java file, wavelength 630e-9.
4. Press "Start computation" to start.
5. Follow the progress in the status bar, when the hologram is 100% completed computation will stop.  Again, takes about 2 minutes on my outdated machine.
6. Select "Real_Binary" output and press "Display output" to display the hologram fringes.
7. Select "File" and "Save" from the menu on the hologram.  Enter a name (eg, testObject_01.gif) to save it.
8. Load the hologram with another program.  Send to a printer and print at the highest resolution (eg, 600x600 DPI).
9. Look through the hologram when illuminating with a tiny but bright non-laser light source or project the image onto a wall by shining a laser-pointer through the hologram

1. Select plate size and resolution.  Let's again select the plate as 600x600 pixels with 423e-7 m spacing.
2. Select the "object.xml" file, wavelength 630e-9.
3. Select randomize phase, "Center plate" should not be checked.
4. Press "Start computation" to start.
5. Follow the progress in the status bar, when the hologram is 100% completed computation will stop.
6. Select "Real_Binary" output and press "Display output" to display the hologram fringes.
7. Select "File" and "Save" from the menu on the hologram.  Enter a name (eg, testObject_02.gif) to save it.
8. Load the hologram with another program.  Send to a printer and print at the highest resolution (eg, 600x600 DPI).
9. Look through the hologram when illuminating with a tiny but bright non-laser light source or project the image onto a wall by shining a laser-pointer through the hologram.

• Don't expect miracles, decent holography film has 5000 lines per mm (127000 lines per inch) but your laser printer has an anemic 600 lines per inch.  Thus, good holography film is approximately 44000 times more dense then your CGH output.  Still, the technique works well enough for you to show your friends and amaze your geek coworkers.
• The reference beam is effectively a plane-wave with an angle of 0 degrees. This arrangement requires the least bandwidth (ie, resolution) in the plate. Unfortunately, the object can't be moved too far from the reference beam because of the low bandwidth available at the output stage. Creating a particularly detailed object may also exceed the output bandwidth. I suggest trying simple objects (eg, letters) initially.
• There are artifacts caused by loss of phase information and quantization of the hologram output.  That's why so many ways to display the output are available in the program.  The physics of a light ray is simulated using complex numbers.  The laser printer (or a film plate for that matter) can only record the intensity of the light so information is lost in the recording process.  And to make matters worse, most output devices modulate intensity in a binary fashion (eg, a pixel is printed or it isn't) and are unable to represent shades of gray.  This further creates artifacts in the final reconstruction.
• This software will be made available as open source under the GPL.  Please support open-source software.  Also be aware that because both the US and UK allow software to be patented this probably means that free software will become unavailable at some point in the future.  The FSF , FFII , and EFF understand these issues, but have an uphill battle against corporate interests and a generally uninformed public.
• When projecting the hologram, make sure that you leave adequate distance between the hologram and the projection screen.  This will ensure that your reconstruction is large enough to be seen clearly.  As specified in meters in the program input, there is an optimal focal distance for your hologram projection.  Also, I suggest you fix the laser, hologram, and projection screen with makeshift mounts instead of trying to hold things steady with your hand.
• Some excellent open-source software is used in this program without modification.  Kudos to beanshell and jdom  for wonderful products.
• This method of CGH calculation is related but not identical to a Fourier-Transform (FT) Hologram. An FT hologram is created by performing a 2-dimensional FT on an image, and then using a lens to perform the reverse transform thereby optically reconstructing the image. If the object is exactly at the plane of the plate, then the method presented here is functionally identical to an FT (but this ray-tracing technique calculates in order=n^2 where a Fourier Transform is more efficient and calculates in order=n*log(n)). However, because in this technique the object does not have to be at the plane of the plate, but can be offset by a specific depth, D. No lens is necessary on reconstruction as the hologram acts as its own lens to focus the image at depth D. FT holograms do not encode depth information. Simply using a 3-dimensional fourier transform is also not equivalent. That said, an equivalent transform (likely similar but not identical to a 3-D FT) almost certainly exists and would calculate much more efficiently, but I haven't seen the math. If you can help work through this, please contact me!
• Strides in computer hardware have enabled brute force numerical simulation to compensate for the simple analytical technique presented here. When I first attempted this years ago, the program ran for 3+ weeks on a microVax II. Now, an equivalent image computes in just a few minutes on my low-end hardware!

Printing the Hologram
Getting the output from the computer program to a transparency which will diffract light is a particularly crucial step in making computer generated holograms.

• When sending the hologram to your printer, you want to reproduce it as faithfully as possible.  That means that you should set both software and hardware (eg, print drivers) to the highest resolution, turn off antialiasing if necessary, avoid image rescaling, etc. I suggest using a graphic program to load and print the hologram so that you have absolute control over printing resolution and rescaling. Your word-processor probably isn't a good choice for this task.
• Better results can be achieved by calculating and printing several adjacent plate patterns, taping them together, and then photographically reducing them (eg, photographing them using a copy stand). I have done this in the past and it does work better since you can move the image off away from the DC component.

Want to help?

• Send me a picture of your best reconstruction using the CorticalCafe CGHMaker.
• Try a better output device than a 600x600 DPI laserprinter.  Many improvements are possible, but the relatively low output resolution is a substantial bottleneck in this technique.  Unfortunately, electron lithography still seems slightly out of reach, but perhaps you have some suggestions or better hardware. 
• Help a student learn about light or tutor someone working on a science fair project.
• Technical suggestions - Unfortunately, I have limited time and can't implement every idea which comes along, but, no doubt, some clever suggestions will improve the results dramatically. 
• A particular improvement that I'd like to see is to modify the n^2 order ray-tracing approach to a mathematical transform of order n*log(n). 
• Take the time to understand things at a technical level... technology is not magic, no matter how amazing it seems.  Read one my philosophies below.
• Tell me what transparency film you are using and rate it so that I can post a summary of what works and what doesn't work.
• See my wishlist.
  

Support Files

• See the precomputed holograms for sample input files including GIF, JAVA, and XML formats.
  

Install Java before running the program
This program is written in Java and should run on almost any modern computer available (Mac, PC, Sun, SGI, etc.). If you are not familiar with Java, please note the following tips:

• Java is a programming language designed to enable programs to be run on virtually any computer without modification. It accomplishes this magic by requiring that only a single program called a Java Runtime Environment (JRE) be tailored to run on each new computer (eg, Macintosh, Windows, Unix). If you don't already have a JRE on your computer, you'll need to get and install it before attempting to use this application.  Most operating systems now come with JAVA installed.  But if it is not already on your machine, you can find it here.
  
• You only need the J2SE JRE (Jave 2 Standard Edition Java Runtime Environment) for your machine. Don't waste your time or hard-disk space downloading the SDK (Software Development Kit) or the NetBeans-Cobundle unless you are a programmer. It won't hurt anything, but is well beyond what you need to run this program.

Neat, but why is this page here? (aka, my soapbox)
I have a passion for science and technology.  But after years of observing how we employ empowering technologies created through our scientific understanding, our technology application seems always to be split between the noble use of creating a more harmonious society (improved quantity and quality of life) and the despicable use of repressing our fellow humans (for social, economic, and political gain).  Although technology seems to take on a life of its own in our fast-paced world, the choice of how we use our technology is anything but a random event.  But without an understanding of science, who will make the decision how we use technology?  Politicians?  Religious leaders?  Corporations?  In the spirit of democracy, I'm hoping that you (yes, you) will play a role in deciding how we use technology.

An understanding of science benefits us all and should be conveyed for what it is:  The scientific method is our best attempt to objectively understand the world around us.  Perhaps an interesting scientific demonstration here, a small discussion of the philosophy of science there, will help us to better understand the technologies we create, thus better understand how we are affected by their consequences.  Whether an artist, an engineer, or a businessperson, a little more objectivity in our perspective benefits everyone.


Disclaimer:  This information including any computer code is presented without any warranty, express or implied.  Use is completely at your own risk.  Mileage may vary.  May result in hair growth or hair loss.