Phase Contrast

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Phase contrast photo by Herbert Highstone

1 Introduction
2 Theory
3 Equipment
4 Procedure
5 Images
6 Foucault to Phase contrast transition

[edit] Introduction

Phase contrast is a test that will show you the optical roughness on your mirror. It is set up exactly like the classic Foucault test with a real (not virtual) slit as shown in Texereau and the old ATM series. Except that in place of the knife edge, you will use a special test device called a phase plate. This test can display optical roughness as small as 1/500 wave high.

It was co-invented by Dr Frits Zernike of Holland and Bernard Lyot of France, the coronographe inventor.

Most of the technical information below originated from Herbert Highstone.

[edit] Theory

In the original theory of the 1930's and 1940's, phase contrast can be understood in wave optics terms by invoking the interference of a reference beam and a test beam. The attenuated and phase-shifted reference beam is created from the zero order frequencies of the slit image. They combine into an averaged wave front as these photons pass through the soot phase strip, which causes a phase lag and also absorbs some of the photons as the averaging process takes place.

The phase lag in the soot phase strip happens because of the same kind of physics that occurs in a microwave lens containing a tapered array of small, spherical obstacles. The soot phase strip consists of an array of tiny soot particles. Because the reference beam must find its along twisting paths around and between these particles, the total path length traversed by the reference beam is longer than the straight-line air path traversed by the test beam. In this way, we can create a phase shift that is extremely useful.

The unattennuated test beam contains the higher Fourier orders (we used to call them diffraction fringes) that sneak around the edge of the phase strip. The phase lag in the reference beam gives a large boost to the interference between the test and reference beams, and thus amplifies the visibility of the phase contrast image.

Attenuation in the reference beam is also needed to improve the contrast of the image. So to get the full benefits of phase contrast, we need both a phase shift and an attenuation of the reference beam. By a lucky accident of physics, the soot phase strip provides both phase shift and attenuation.

We can easily see that wave optics and Fourier optics ideas must be combined to account for what we see when we do the test. For example, Fourier optics and image processing concepts are needed to explain the changing properties of the phase contrast image as the phase strip is moved across the slit image.

[edit] Equipment

Fixture for making a phase plate

Herbert Highstone's Setup. Slit is from Surplus Shed. Large finder scope or camera lens is necessary because the eye opening is too small to capture the image.

Dale Eason's setup. The light source is a slide projector with a slit taped over the lens. The projector should have been moved closer to the phase plate to prevent astigmatism in the setup. It created uneven lighting and was moved as close as possible to the phase plate. The phase plate was made on a microscope slide. Later version used a 3inch square plate of glass.

[edit] Procedure

Phase Plate

To make the phase plate pass the glass over the candle 5 to 6 times. Scrape away one side of the soot strip to make a sharp edge. A sharpened wooden strip, sharpened with a chisel like edge will do when run along a straight edge. Leave the soot strip at least 5mm wide.

The attenuation of the carbon phase strip will increase the sensitivity of the test by tending to emphasize the fainter Fourier information. However, this density increase eventually reaches a point of diminishing returns due to an excessively faint image and also problems with stray light in the system. I find that a phase strip that transmits about 5% of the impinging light is best for ordinary work.

Additionally, the classic, wave-optics analysis of phase contrast states that the increase in sensitivity is proportional to the square root of the optical density of the phase strip. Thus you will dim the image much faster than you can increase the sensitivity of the test. Once again, you must settle on a compromise that is suitable for your own personal use of this test.

Phase plate calibration

This step is not needed but helpfull if you have the correct simple equipment. If you don't have the equipment then just try various densities until you find one that works.

Texereau shows phase contrast images taken with phase plates of densisties 1.69 to 2.81. Here is one way to measure the density of a plate. Mount a Cds cell (light variable resistor available at Radio Shack) behind a small 1/16 inch to 1/8 inch hole. Use an ohm meter to measure its resistance at a constant light intensity. Place the phase strip in front of the hole and measure the resistance. Compare that reading to one from the following:

- Kodak Seperation Step tablet T27 http://www.bhphotovideo.com/bnh/controller/home?
- http://www.tiffen.com/displayproduct.html?tablename=kodakaccessories&itemnum=EK1101484
- Stouffer Step wedge http://www.stouffer.net/TransPage.htm.

These are calibrated in density units the same as specified in Texereau. Move the strip in front of the Cds cell until you find a similar ohm reading.

Setup

Setup is similar to standard foucault except the phase plate replaces the knife edge. Only one edge of the phase strip is used. A very narrow slit of about 50 microns and a very bright soucrce is needed. A surper bright LED can sometimes work but the exposure times will need to be increased to a few seconds. You can even take foucault imges using the soot knife. Move the stage until the 70% zone nulls. That usually set the knife edge at its best focused image. Move the soot knife until the slit is just at the side of the soot. Use you eye from behind the soot to align the soot and slit image parallel to one another. Next use the scope or camera view finder and move the soot knife into the beam until the foucault image just vanishes. Now you should see the phase contrast surface detial. It can sometimes be hard to see in the camera view finder. Assuming you have a digital camera take a picture and see how it turns out. The image processing that goes on in this test can be easily confirmed after you have just barely moved the zero order slit image onto the soot phase strip. When you are at this exact position, you'll see that the bandpass of the test in terms of spatial frequencies is at its widest. I.E., you'll see a wide variety of spatial frequencies on your mirror, ranging from narrow Foucault zones to some amazingly fine optical texture. But as you move the slit image farther onto the phase strip, you'll also be moving the closer diffraction fringes onto the sooty strip, thus making them a part of the reference wave. And when this happens, you'll discover that the lower frequencies fade away rapidly, and now your image will display only the finest surface textures on your mirror.

[edit] Images

10 inch F5 Phase contrast on the left, Foucault on the right. The Foucault image shows considerable surface features. It reminds me of images of Neptune. Similar features and others with more detail can be seen in the phase contrast image. Photos by Dale Eason

Foucault and phase contrast images of an 8 inch F7 with surface ripple visible in the Foucault image as well. Photos by Dale Eason

18 Inch F5 high quality mirror showing a near perfect Foucault image. Phase contrast shows some marks. Many of these can be seen in the dusty coating on the surface so it is uncertain what is surface details and what is caused by dust. Photos by Dale Eason

Welcome to the brown planet. The weather today calls for some high cirrus close to the equator with small puffy local cumulus in the hilly northeast. Frost will remain close to the night side of the planet while hurricane Dale will be active in the southern equatorial region as darkness approaches.

Phase contrast image of 16 inch F5 plate glass had figured by and photographed by Dale Eason. The cirrus effect was created by not inserting the phase knife all of the way to block the primary slit image. It is what is left of the Foucuault image. The hurricane on the right equator is a clamshell fracture on the edge of the mirror.

Closeups show the difference between dense a less dense phase strips.

1.45 optical density phase strip

1.3 optical density strip

6 inch F6 by Mike Lockwood.

A mirror by Carl Zambuto that has been in a scope for 3 years. The long vertical streak just left of center is in the dust on the surface.

[edit] Foucault to Phase contrast transition

The phase knife can be used as a Foucault knife by not inserting it into the return beam as far as needed for a phase contrast image. The following sequence shows a transition from Foucault to all phase contrast image as the knife was moved into the beam further for each picture. This F2 sphereical mirror has a pattern etched into the glass. The cause is believed to be the paper towel it was wrapped in for 30 years. These images were all made using a super bright white LED taken from a flashlight. The slit was .001 inch wide. The camera was a Nikon D40 digital SLR with a 70mm lens. Exposure time was 20 seconds at ISO 200. <P> As the knife moves more into the beam the low frequency spacial detial vanishes and only the narrow high frequency detail remains. The most detailed view of a given area is where the white wisp of Foucault detail starts to vanish and is replaced by the red toned phase contrast image.