Amnon Silverstein
Hewlett-Packard Laboratories
Draft Dec 10 1996
Dec 13: Appended polarizing filter to parts list
Dec 16: Added equations for FOV, Magnification, etc.
The PSM is a device for estimating the perceptual strength of an image in units of 'times-threshold'. It works by reducing the contrast of the image until the operator subjectively judges the pattern to be 'barely-visible' or 'just-acceptable', or to be at any other criteria strength. The reciprocal of the amount of reduction is the strength of the original image in units of times above the threshold contrast. For example, if the operator needed to reduce the strength of a halftone pattern to 1/5 of its original strength for it to have an acceptably low contrast, the unreduced pattern was at 5 times the acceptable level of contrast. The PSM is suitable for hardcopy, video, or practically any other sort of pattern generator. The PSM can be used to estimate the strength of halftone patterns, banding artifacts, and other patterns. The PSM can only estimate the perceptual contrast strength of a pattern, but not how annoying a pattern may look. It is not suitable for estimating the appearance of visible artifacts. It is best suited for tasks such as judging printer artifacts on plain swatches, and not artifacts on printed images (such as compression artifacts).
The typically used definition of contrast in vision science is:
max([(intensity of a point on the pattern)-(mean intensity))]) / (mean intensity)
where: [] is the absolute value function, max is the maximum value function, and the mean intensity is the spatially averaged intensity of the image.
For example, a white bar (intensity=10) on a gray background (intensity=5) would have a contrast (10-5)/5 = 100% contrast. A sinusoidal grating that has a peak of intensity 3 and a trough of intensity 1 has a contrast of (3-2)/2 = 50% contrast.
A more useful definition of contrast uses a local neighborhood around each image point. A Gaussian window can be used to average the area around an image sample point. The local contrast provides a better indication of the perceptability of a pattern. For example, sensitivity to a small Gabor patch will not be decreased be a bright but distant anular surround as much as a bright but close anular surround. The local contrast decreases when the surround is close, but not when the surround is distant.
When viewed through the PSM, the contrast of a pattern is optically reduced. The reduction in contrast is achieved by mixing a sharply focused image of the pattern with an optically blurred image of the same pattern.
The blurred image is highly defocused, and is hence spatially averaged over a large visual angle. The blur-circle size depends on the size of the pupil. It can be set so the blurred image contrast is essentially zero for the spatial signal content of the stimuli.
By mixing the focused image (which had the same contrast as the pattern) with the zero-contrast image, we create a stimulus that has a contrast that is reduced by the mixing ratio relative to the original pattern. For example, if we created a stimulus that was 10% pattern and 90% blank, the stimulus had 1/10 the contrast of the original pattern. The stimulus is identical to the pattern in all respects except that its amplitude relative to its mean is reduced. The stimulus is not a blurred version of the pattern.
Mixing is achieved by means of a polarizing beam splitter cube. The sharp image and the defocused image are cross-polarized and superimposed on an aperture. The subject views the combined images through an ocular lens that is a focal-length away from the aperture. The entrance pupil of the subject's eye is positioned at approximately the focal point of the PSM's ocular lens, so the focused image and the defocused image have approximately the same magnification [Ref Badel Optometer]. The aperture forms a black surround.
The mixture of the two images is controlled by rotating a linear polarizing filter. When the filter is oriented so that its axis of polarization is vertical, the subject sees an image of the pattern at almost 100% contrast (with a very slight loss of contrast due to leakage of the filter and the beam splitter). By rotating the filter away from vertical, the mixture of the sharply focused and the blurred image varied as the cosine-squared of the filter angle. This means of mixing the images did not change the color, luminance or magnification of the stimulus. It is important to note that the mixing procedure does not blur the stimulus. The only effect of rotating the filter to reduce the stimulus contrast.
The basic plan of the PSM is quite similar to a Keplerian telescope. An objective lens forms an inverted image of the test pattern on an aperture stop. The image is viewed through an ocular lens configured as a columnated magnifier, so the image is at the focal-point of the ocular. However, in the middle of the system is a relay lens, that copies the image formed by the objective across a span. The purpose of the relay will be described later.
If the entrance pupil of the eye is at the secondary focal point of the ocular, then the system can be used as a Badel optometer. That is, the vergence of the light entering the eye can be adjusted by moving the image formed by the objective away from the focal point. If this is done, neither the image size or brightness is changed. If the image is moved away from the eye, the vergence of the light entering the eye is positive. If the observer has corrected normal vision, the observer can not accommodate to this stimulus, and hence will see the image as blurred.
The PSM forms a pair of images. One image is at the focal point of the ocular lens, and the other is displaced along the optical axis away from the eye. The pair of images is created by splitting the light with a beam-splitter and forcing half of the light to take a longer path.
A set of two splitters and a right angle prism are configured as shown in the diagram to form an optical unit called a 'maze'. Half the light is diverted at a right angle from the optical axis with a polarizing beam splitter. It is then turned around a corner and sent back towards the optical axis by a right-angle prism. It enters a second splitter which is angled to send it back along the optical axis. Since it was polarized when it reflected off of the first splitter, nearly all of the light is reflected back onto the optical axis.
![[Close up of maze-unit]](psm2.jpg)
The half of the light that went straight through the first splitter continues into the second splitter. Since this light was already polarized by the first splitter, it passes straight through the second splitter unaffected. This light followed a direct path, and converges to form an image at the stop. The other half of the light followed an indirect and longer path, and thus forms an image before reaching the stop.
The relay lens has several purposes. First, it provides space for the maze. Second, it makes the angles of the light cone that pass through the splitter small. If light rays pass through the splitter at a larger angle, the splitter loses efficiency, and (even worse) loses efficiency differentially depending on wavelength, so the two images end up colored.
The pattern (P) is combined with a highly defocused coppy of itself, the blank (B). The output image (P') is a mixture of the two that is determined by the angle (theta) of the polarizer.
P' = P cos2 (theta) + B sin2 (theta)
The contrast (C) of P is determined by its amplitude around its mean. Since B is the spatially averaged copy of P, B is the same as the mean of P.
C= (P-B)/B
The contrast of P' is also determined by its amplitude around its mean (B'). Since P and P' have the same mean:
B' = mean(P') = B
And therefore:
C' = (P' - B)/ B
Hence, the relative contrast of P' to P is:
C'/ C = (P'-B)/ (P-B)
= (P Cos2(theta) + B sin2(theta)/ (P-B)
=(P-B) cos2 (theta)/(P-B)
=cos2(theta)
Note that the relative contrast depends only on the angle of the filter, and that the color and intensity of the pattern do not change.
The instrument does not have a built in light, because if it had one the subject would not be adapted to the light in the instrument. Make sure you have the subject and the instrument in the same light, and the subject should be given time to adapt to the light.
The field of view is:
2 arctangent((aperature diameter / focal length of ocular)/2)
The diopters of convergence exiting the ocular are:
Dexit = (1/focal length of ocular) - (1/(focal length of ocular + extra maze length))
The diopters of blur at the eye are:
Deye = 1/((1 / Dexit) - distance ocular to eye)
where distance ocular to eye should be equal to the focal length of the ocular.
Using a thin-lens approximation, the diameter of the blur circle on the retina is:
dBlur = diameter of subject's pupil * (Deye + Peye)/ Peye
where Peye is the power of the eye (around 100/3)
The visual angle of the blur circle is:
2 arctangent((dBlur/ diameter of eye)/2)
where the diameter of the eye is around 3 cm.
If the PSM is adjusted so the ocular is closer than a focal length from the iris, there will be divergent light at the eye (also called a stimulus to accomodation). If the ocular is further than its focal length from the ocular, the light will be convergent at the eye. For most purposes it will be best to have the ocular one focal length from the iris, so the light is columnated (has zero vergence).
It is better to correct the subjects vision with spectacles or contact-lenses, but it is also possible to correct for myopia or hyperopia by adjusting the ocular. This will not correct for astigmatism, however. If the subject is allowed to set the correction, he or she is likely to set it to over or under correct. This can cause eye strain and it can blur the stimulus.
Another reason one might want to adjust the ocular would be to create a stimulus to accomodation that is in agreement with the simulated viewing distance. However, if the subject does not have the ability to accomodate to near objects (which is highly probable if the subject is over 40 years old), the subject will not be able to see the stimulus in sharp focus without a corrective lens. If the subject viewed the printed sample under natural conditions, there would be a stimulus to accomodation of:
1/(sample distance(meters)) Diopters
To set the vergence of light at the eye, the iris should be moved from the focal point of the ocular:
Id = Distance of ocular from iris.(meters)
Fo = focal length of the ocular (meters)
vergence at eye = (Id/ Fo^2)
If the instrument is set up exactly right, the relay lens should form a 1:1 image. To find the exact magnification, it is better to make measurements than to just do the math.
M1 = The magnification from the objective lens for the image on the iris is
Td = distance of test pattern from the principal plane of the objective.
Fobj = focal length of objective in meters
Foc = focal length of ocular in meters.
M1 = (-1/Td) / (1/Fobj - 1/Td)
Note: Since this will be negative, the image is inverted.
If the ocular is set up as a columnated magnifier, the eye views the iris and the direct image at an effective distance of Foc.
The stimulus will have an angular magnification equivalent to the pattern viewed at a distance of:
Foc / M1
Or, more usefully:
Equivalent viewing distance = (Foc/Fobj )* Td - Foc
Newport Corp 1791 Deere Ave Irvine CA 92714 800 222 6440
| Count | Part | Page # | Desc | Price 1994$ |
| 1 | URL-36 | Optical Bench | $268 | |
| 1 | RSP-1T | Rotation Stage | $117 | |
| 1 | SS-1 | Spacer Set | $16 | |
| 2 | 10FC16PB.3 | 2.40 | Beam-Splitter Cube | $418 |
| 1 | PO46N-50 | 11.56 | Prism stage | $337 |
| 1 | LM-2R | 11.45 | Lens Holder | $39 |
| 1 | LH2-150R | 11.45 | Lens holder | $26 |
| 3 | RB2-LM2-2 | 10.26 | Riser block | $18 |
| 1 | RB-LM1-2 | Riser block | $19 | |
| 4 | BP-2 | 10.27 | Base Plate | $18 |
| 1 | BP-4 | Base plate | $24 | |
| 2 | CLM-N 11.48 | 11.48 | Lens Mount Ring | $103 |
| 1 | ID-1.0 | 11.58 | Iris | $88 |
Edmund Scientific 101 East Gloucester Pike Barrington NJ 08007-1380 USA 609 573 6250
| Count | Part # | Page | Desc | Price |
| 1 | A32529 | 61 | Prism | $69 |
| 1 | A43786 | 84 | Polarizing Filter | $13.50 |
Other stuff
Nikon 50mm $95
Tokina 28mm $100 (Nikon mount)
American fasteners
Mounting tape
A small project box
Note: In the photos I have the maze on the wrong side of the relay. It will work like that, but the math isn't as straight-forward. I'd build it with the maze on the other side if I did it again, as in these instructions.
Note: Get absolutely no finger prints on the cubes or the prism! It is best to wear optician gloves when messing with them. Be sure to clean all the machining oil off of the project box before you install the optics.
Make a paper template in the shape of the maze optics and put it on the floor of the project box. Position the project box on the prism stage so the splitter cubes will be centered on the optical axis. Find a place to drill a hole through the project box where a button-head screw can be used to attatch the box to the prism table. The prism table has pre-drilled and tapped holes. Center-punch the sides of the project box at points that correspond to the centers of the splitter cubes. Drill 7/8" holes at these points. Use thin mounting tape to attatch the optics to the floor of the project box. Mount the project box to the prism table. I only found room for one mounting screw, so I first attatched the project box to the prism table with mounting tape, and then I fastened it with the screw.
Attatch the rotation stage to the edge of the optical bench. Use spacers from the kit to put it at a 2" optical axis height. Put the ocular lens mount on its stand-off and base-plate. Put the Nikon lens into the holder and adjust the focus so the lens is out as far as it will go. Mount the holder to the rail as close to the rotation stage as possible. Mount the iris on its stand-odd and base plate. Place it so the iris is as close to the back of the ocular lens mount as possible.
Drill and tap three 120 deg set screws into the holder for the relay lens. The holder isn't deep enough to use the included ring. Put the lens holder on its base. Install the relay lens.
The relay lens should be positioned so it is a 1:1 relay. I fiddled with it, but it should be positioned so its principal plane is 2 focal lengths away from the iris. Part of this distance is in glass, so you need to take into account the index of refraction of the splitters.
The distance from the back of the lens to the iris should be:
dIris= (F * 2) - (F-BFL) - dCube + (dCube * rCube)
Where
So, dIris = 269mm
The maze should go as close to the relay as you can get it. Mount the objective lens, and put it so that it forms an image: dObjective = (F * 2) - (F-BFL) = 242.5 from the back of the relay lens. Where it forms an image depends on how far away you want to put the test pattern.
Align all the optics. Put a point-like light source where you want to put the test-pattern, centered on the optical-axis. Tape a white bit of paper on the center of the iris. You will get two images, a sharp dot and a big dot. Adjust the knobs on the prism table, and adjust the lens angles until you get the sharp dot centered in the large dot, and both also centered at the center of the iris. Put a test pattern in and look through the instrument. Adjust the ocular so the lens is as far in as you can make it with the pattern still in sharp focus (probably all the way in). Set the rotary stage at 90 deg. Loosen the retaining ring. Put the point-like light back on the axis. Dim the room lights. Rotate the polarizer filter in the mount until you see only a blurred light with no sharp center. Tighten the retainer.
The PSM can be used for many types of experiments.
You can use this method with the PSM to estimate the strength of the patterns in units of times-threshold. Give the subjects written instructions on what you would like them to do. For example, you may want to have them adjust the pattern until some printer artifact is just barely visible. It is important that you write down your instructions so different subjects are given the same instructions and you have a record of what instructions were given. It is also better if you do not encourage too strong a criterion for visibility. If you insist that your subjects adjust the dial so they are positive they see no pattern, they will just set the dial to zero for every pattern.
Randomize the order of presenting your stimuli, and do not allow the subjects to change the adjustment of the dial after they have made a setting. It is best if an experimenter records the settings, but if you are recording your own settings be careful to make up your mind before you look at the reading or your results will be confounded by your expectations.
Improved accuracy is sometimes found with the method of ascending and descending limits. Start the contrast at zero, and only allow the subject to adjust it upwards until the pattern is visible. Then set the contrast to 100% and only allow the subject to adjust the contrast down. Average these two measurements together.
The subjects were instructed to adjust the contrast until the pattern was just visible. The subjects were allowed to adjust the contrast up and down for any amount of time. The order of presentation of the stimuli was randomized by the experimenter. After the subject finished adjusting the contrast, the experimenter recorded the contrast level. The pattern and the subject were illuminated with the same ambient tungsten light so the subject remained adapted to the light source that illuminated the pattern. To compare results between subjects, you will need to determine a scale-factor to make up for the difference in the subjects' criteria.
You can use the PSM to make quality assesments at different contrast levels by having the experimenter change the pattern while the contrast reduction factor is set at a constant level. This way you can measure the discriminability of two patterns at a certain level, or the objectionability as a function of contrast. I have been developing some methods that I will describe elsewhere.