Open aperture holograms w/lens

[Joe Farina]

A forum member kindly provided me with a 12-inch plano-convex lens, and I want to experiment with it.

I've never done an open-aperture hologram, and wanted to try the attached layout in Practical Holography, by Saxby, 2nd edition, page 230. I was wondering how such a hologram would compare to a standard Denisyuk or split beam reflection hologram in terms of image quality. As an image-plane hologram, I would expect it to be brighter. I was wondering about the possible depth of the image, which I've read is quite shallow (stated in Holography Handbook). Also, I wondered about possible distortions of the image. Thanks in advance.

[Din]

One of the problems that plagues display holography is the plethora of names for specific types of holograms. This is the case here, where "open aperture holograms" in Saxby is not "open aperture holograms" in the Handbook. The phrase "open aperture hologram" or "achromatic hologram", as described in Handbook, refers to a hologram made with an H1 -the aperture - which is not restricted when recording an H2 - you use the entire H1, as opposed to the case when the H1 - the aperture - is restricted to a slit for a rainbow hologram. The slit in a rainbow hologram is to "stop down" the aperture (here 'aperture' and 'stop down' is used in the photographic sense), which, as is well known, increases depth of field (https://www.adobe.com/creativecloud/pho ... ength.html). The fact that decreasing the aperture increases depth of field is also true in holography, where the narrower the slit, the deeper is the focused image. In holography, if you do not restrict the aperture, ie use the entire H1, then you lose depth of field and the image starts aberrating very close to the image plane of the H2 due to dispersion; there is zero dispersion right at the image plane which increases as the image distance changes from the plane. Effectively, you have about 1/2 an inch on either side of the image plane for a focused image. In about 1981 Kaveh Bazargan created a "dispersion compensation" system to compensate for the dispersion and so increase the depth of field, so the company whose research group he headed (and in which I was a researcher) increased the depth of field to several inches.

The type of "open aperture hologram" described in Saxby is generally referred to as a "one step hologram" - there a variety of holograms called 'one step' and sometimes a contact copy is also referred to as 'one step'; see comment above about the different names ( some people hold an almost religious attachment to some names and get angry when they perceive a name as being misused!). However, getting back to Saxby, the idea of the one step is that an image plane hologram can be recorded without an H1, by imaging the subject - focusing the subject - via a lens or curved mirror - most of the literature uses curved mirrors to focus the subject. You then place an H2 plate into the focused image and record a single, image-planed hologram.

The image in a (Saxby) open aperture hologram can be quite bright in theory, but there a number of issues. Firstly, most of the illuminating light on the subject needs to go through the lens, any light not going through the lens will not be recorded. However, it's quite difficult to illuminate a subject on-axis to a lens to meet this condition unless the light source itself is also on-axis, in which case it'll be between the hologram and the subject. If you illuminate the subject with an off-axis source, depending on the geometry of the subject, most of the reflected light will not go through the lens. So, you need to choose your subject matter carefully. Secondly, Saxby uses a 2f-2f geometry because a 2f-2f geometry will not magnify the image - you get a one-to-one relationship between object space and image space. However, for an extended object (such as a cat) it's impossible to exactly get a 2f-2f geometry - some parts of the cat will be nearer to the lens than 2f and some will be further away. This will distort the image causing lateral magnification - the depth of the cat will decrease relative to the actual model. Finally, there are what are called Seidel Aberrations. These are: spherical aberration, coma, astigmatism, field curvature and distortion. These aberrations arising from the lens imaging the cat, depend on the depth of the cat model, and the height of the cat model above the lens axis; see below for an illustration of the Seidel aberrations. To avoid Seidel aberrations, the model needs to be thin and small relative to the lens aperture - 12 inches in your case. The worst of the Seidel aberrations in display holography will be field distortion - the cat will seem to be bowed outwards - and lateral magnification - the cat will appear 'stunted because it's height-to-depth ratio will be wrong. Remember also, that a mismatch between reference beam and reconstruction beam will cause holographic aberrations independant of the Seidel aberrations. I wrote a paper on holographic aberrations based on the pioneers in holographic aberrations - Meyer and Champagne. So, if you need further information let me know.
By the way, completely off-subject, if you ever see a movie where a character is riding towards you from a distance who doesn't seem to grow while approaching the camera, this is because of the difference between lateral and transverse magnification. David Lean used the effect stunningly with a purpose-built lens ever after called the "David Lean lens".

Seidel.jpg (56.34 KiB) Viewed 13291 times

[Joe Farina]

Wow, tremendous summary of the important points! Thanks!