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Introduction

Amateurs are concerned with the calculated effects of diffraction caused by the secondary obstruction on image contrast. Much has been written on the effect of diffraction by the secondary in amateur circles. Very little has been published in professional journals concerning the diffraction effects of the secondary obstruction. I could find nothing published on how much secondary diffraction actually effects observation when the total optical system and human vision are considered. The literature suggests there are many problems that contribute more significantly to the loss of contrast and resolution than the effects secondary diffraction.

After researching the literature on optical design, diffraction, and the human eye the following conclusions can be made about resolution and contrast for visual observation.

1). The perception of contrast by human vision is largely subjective and dependent on factors that are unrelated to the objective measurements of image contrast, (Ratliff, 1972). Defects in the human eye can contribute significantly to loss of contrast, (Douglass, 1897).

2). A very large central obstruction improves the resolution of a telescope when splitting double stars of similar brightness, (Dall, 1938) and (Whysong, 2004).

3). The total energy contained in the disk and first ring is under one arc second for an 8” Schmidt-Cassegrain, which means the loss in contrast is not observable under normal seeing conditions and probably not observable in 1 arc second seeing, (Whysong, 2004). The total change in energy due to the shift of luminance due to the secondary is below the detection threshold for the vast majority of people

4). High magnification causes a visually observable loss in contrast even with unobstructed telescopes, (Douglass 1897).

5). Seeing is the single most important component for high resolution observing, (Douglass, 1897), (Dall, 1938) and (Everhart 1959).

6). Other imperfections such as, air currents, alignment, optical aberrations, optical coatings can contribute more to loss in contrast than the secondary obstruction.

Contrast

An understanding of the effects of contrast from the secondary obstruction must start with an understanding of contrast and how the human vision perceives and interprets contrast in an image. Contrast and contrast sensitivity may be defined in the following manner,

“Contrast is the difference in brightness that separates an object from its background. Contrast sensitivity is a person's ability to identify an object from its background.” [1]

Seeing contrast is dependent on the individual observer and cannot be easily described by optical theory. People do not perceive contrast as a function of the energy distribution, (brightness or darkness), of the observed object. Rather, seeing contrast is similar to other aspects of how we perceive our environment with vision. Our ability to see contrast, shadows, shades of gray, motion, intensity, and color are all dependent on the context around and within the object we observe. Human vision is a function of comparisons; it is subjective. Not a function of the objective measurement of changes in brightness.

1. Human Vision

There are very few astronomically related articles exploring how the eye effects observation. The effect of vision on telescope performance is certainly a neglected area. The human eye can contribute significantly to loss of contrast, especially as the eye ages, (Douglass, 1897). Even though there is little information written about human vision and how it effects observation in astronomy, there is a great deal written on visual perception outside astronomy. From research on human vision we can gain an understanding of vision's role in observational astronomy.

The Eye

As we age, the eye and our ability to see degrades. Focus becomes more difficult, the lens tends to cloud and scatter light; we loose the ability to see in low light conditions; we loose the ability to see contrast. We also work at a telescope with a fully dilated eyes. A fully dilated eye suffers from considerable spherical aberration. Anyone who has returned from the Optometrist with a dilated eye knows how poor vision is with a dilated eye. Other optical defects in the eye, like astigmatism, contribute to the poor quality of the human observed telescope image. If you ware glasses the poor optical quality of typical eyeglasses will contribute to image degradation. Plastic lenses may also be heavily scratched contributing to scattering of light.

The ability to see contrast in low light conditions can be summed up in this way, “Can someone have both good vision under high contrast conditions yet poor visual performance under low contrast conditions? Yes. Many people can read the 20/20 line on the Snellen chart yet still complain about visual difficulties under low contrast conditions, such as driving at night. Such poor visual performance may be caused by normal variation, age, ocular disorders or ocular pathology.” [1]

Vision and contrast

The ability to perceive contrast is not necessarily related to a real variation in the intensity of illumination. It is related to how the eye physically reacts to the variation in illumination and how the brain processes the information it receives. Ratliff, (1972), explains the situation in this manner, “Without Precise physical and psycho-physical measurements it is difficult to tell how much of the contrast we perceive is objective and how much is subjective”.

Given the definition of contrast and Ratliff’s assessment one would suspect the contrast we see in an object is not simply related to a physical phenomena, such as the change in brightness. Instead, it is related to physical processes in the eye and how our brain processes the information. As a result of the human brain's interpretation of the properties of an image, seeing planetary detail is not simply a function of the image presented by the telescope in the form of airy disks and diffraction effects. It is far more complex than simply calculating the theoretical properties of a diffraction pattern.

Neutral-Color Perception

The ability to determine contrast is dependent on the brightness of the surrounding area and other characteristics of the object. The effect on contrast due to the illumination of the surrounding area can be demonstrated by projecting a large dognut of uniform illumination on a wall. Figure 1.

Figure 1, NEUTRAL-COLOR PERCEPTION depends largely on the ratio between two different light intensities in adjacent regions, as demonstrated with a ring and disk pattern projected by two lanterns in a dark room. In this experiment the light in the disk is kept constant but the ring light is increased, changing the appearance of the disk from white to dark gray. The ring-to-disk ratios are (top to bottom) one to three, two to one, four to one and eight to one. These photographs show how the ring and disk colors appear to an observer.

A small disk is projected in the center of the large dognut. If the large donut's illumination is dim the inner disk will appear to be white. If the dognut's illumination is varied from dim to bright, without changing the illumination of the small inner disk, one will see the small inner disk vary from white to dark gray. The apparent change in contrast will happen despite the fact that the small inner disk's illumination does not actually change in intensity, (Wallach, 1963). In this case the perception of contrast is a function of the ratio between two light intensities in adjacent regions.

Mach Bands

Ratliff, (1972), illustrates another subjective contrast phenomena called Mach Bands. These bands can be produced with any shadow that is reasonably dark, Figure 2.

Figure 2, MACH BANDS can be produced with light from an ordinary fluorescent desk lamp (upper illustrations). Place a sheet of white or gray paper on the desk and the light about a foot or so above it. Covering the ends of the lamp, which usually are not uniformly bright may enhance the effect. Turn out the other lights in the room and hold an opaque card an inch or less above the paper. Various positions should be tried for optimum results. Note the narrow bright line and the broader dark line at the outer and inner edges of the half-shadow; these are the mach bands. The lower illustration is a photograph of a half-shadow produced by the method described. The reproduction of the photograph does not retain all the characteristics of the original because of losses inherent in the reproduction process.

An opaque card blocking light form a lamp in a dark room can produce a mach band. You will see a slight increase in the illumination just prior to the beginning of the shadow. Followed by a uniform drop in illumination with a sharp drop in brightness seen as a dark line just before the shadow becomes uniformly dark. The actual illumination curve and the perceived illumination curve are shown in Figure 3.

Figure 3. OBSERVED BRIGHTNESS CURVE obtained by psychophysical measurements (black line) has two sharp flections, one corresponding to a bright band and the other to the dark band. Measurement of the actual luminance (colored line) across a half-shadow region reveals that the effect lies in the eye of the beholder and in not an objective phenomenon.

The real image intensity as the shadow transitions from light to full shadow is absolutely linear. No lines exist. The perceived contrast difference is an illusion. Ratliff, further reports that Mach Bands have been mistaken for diffraction effects by W. K. Rontgen.

Mach bands can also be observed within a series of lines, Figure 4.

Figure 4, MACH BANDS PHENOMENON created with horizontal lines is shown here. In the illustration at left the black lines are a constant thickness from the left side to the midpoint and then thicken gradually. When the illustration is viewed from a distance, a vertical white “Mach band” appears down the middle. In the illustration at right the horizontal black lines are a constant thickness from the right side to the midpoint and then thin out. When viewed from a distance, the illustration appears to have a vertical black band down the middle.

The image on the left has lines that are of constant thickness from the left side to the midpoint. From the midpoint the lines gradually thicken. The image on the right has lines that thicken from the left edge to the midpoint. From the midpoint on the lines are of constant thickness. If the images are viewed from a distance a vertical white Mach band will appear down the middle of the series of lines in the left image. A black Mach Band will appear in the right image.

Dark Spur

A contrast effect that may have interesting applications for astronomy is having a Dark Spur between two areas on unequal brightness. The Dark Spur is an abrupt drop in luminance followed by a gradual increase in luminance Figure 5.

Figure 5, DARK SPUR between areas can create brightness reversal. Objectively the area at left of the contour is darker than the area at far right, but to an observer the left side (here simulated) will appear to the brighter than the right side. This brightness reversal agrees with the extrapolation (colored curve) from the maximum and minimum produced by inhibitory process (black curve at right).

The Dark Spur can result in a reversal in the perceived brightness from the real brightness of the two areas separated by the Dark Spur. This means the darker area will appear brighter even though it is in fact, darker. This effect is illustrated in the image of the vase in Figure 6.

Figure 6, KOREAN VASE form the 18th century provides an excellent example of the effect of a dark spur between areas. The moon appears to be brighter than the sky directly below it, but the actual luminance is just the reverse. If only a portion of the moon and an equal portion of the sky about one moon diameter below it are viewed through two identical small holes in a paper so that the dark contour is masked, the moon appears darker than the sky.

The moon at the upper center of the vase is in fact darker than the area directly below it even though it appears the moon is brighter. A similar effect might be seen when examining a crater with a dark band around it. The observer might be fooled into believing the crater is lighter than the surrounding terrain when, in fact, the crater is darker.

Craik-O’Brien Effect

The appearance of differences in the luminance near a contour can produce the illusion that two areas along the contour are of different illuminations when in fact the luminance is the same. In other words, contrast is produced where no contrast actually exist! This effect is called the Craik-O’Brien Effect, Figure 7.

Figure 7, LUMINANCE on both sides of the Craik-O’Brien contour is the same but the inside (here simulated) is brighter. The human visual system may extrapolate (colored curve) from the maximum and minimum produced by inhibitory processes (black curve at right).

The Craik-O’Brien contour is illustrated in Figure 8.

Figure 8, CRAIK-O’BRIEN EFFECT (this example is known as the Cornsweet illusion) is the result of a specific variation of luminance at the contour, which makes the outer zone appear slightly darker even though it has the same luminance as the inner zone. The effect here is less than in the original because of difficulty in reproducing the actual intensity relations.

In this example, the outer portion of the disk appears to be darker than the inner portion despite the fact that the two areas have the same luminance. The Craik-O’Brien effect can be negated by placing a wire along the contour, Figure 9.

Figure 9, SOURCE OF CRAIK-O’BRIEN EFFECT can be demonstrated by covering the contour with a wire of string. When this is done, the inner and outer regions appear equally bright.

Doing this will reveal the two sections as having the same luminance. An example of the Craik-O’Brien effect is the Japanese Ink painting in Figure 10.

Figure 10, JAPANESE INK PAINTING, Autumn Moon by Keinen, has a moon that objectively is only very slightly lighter than the sky. Much of the difference in apparent brightness is created by the moon's contour. The extent of the effect can be seen by covering the moon's edge with string. The painting, made about the 1900, is in the collection of the late Akira Shimazu of Nara in Japan.

The moon in the painting is only slightly lighter than the surrounding sky despite the appearance of being much brighter. Placing a string around the moons edge will reveal the real luminance of the moon.

The final example of how contours can effect the perception of contrast is of Chinese Ting white porcelain, Figure 11.

Figure 11, CHINESE TING YAO SAUCER is an example of the famous Ting white porcelain produced in the Sung dynasty of about A.D. 1000. Although the entire surface is covered with only a single creamy white glaze, the incised lotus design appears brighter than the background because of the incisions, which have a sharp inner edge and a graded outer edge, producing exactly the kind of contour that creates an apparent difference in brightness.

The plate is covered with a uniformly white glaze. The difference in contrast is an illusion created by the contours from the incision in the plate used to create the lotus pattern.

These examples of different contrast effects and illusions demonstrate the ability for an observer to see contrast, is not a trivial problem. The contrast we see is subjective not objective. The fact that we see any detail in low illumination situations is more a tribute to human vision than to the optical properties of a telescope. Given this brief description of the way human vision perceives contrast, the reader should start to realize there is more to seeing contrast than just diffraction effects caused by the secondary. Contrast is largely a product of human vision and is often contrary to the real luminance of a scene.

Color Perception

We perceive color in much the same was as contrast. The color we see is not necessarily the color indicated by a objective measurement of the spectrum of the object. We experience color not simply as the spectrum of measured colors but as a comparison of all of the color information in the scene. We have all experienced this effect when painting a room. The color the walls appears to be is dependent on all of the colors in the room. The luminance around a color can also effect the perceived color. Figure 12 illustrates the effect of luminance on the apparent color of the inner disk.

Figure 12, CHROMATIC COLORS also vary in lightness depending on the intensity of the illumination in an adjacent region. The experiment simulated here shows how the appearance of a disk of orange light changes with the intensity of a neutral surround. In this case increasing the intensity of the ring changes the apparent color of the disk to brown.

The perceived color can be changed simply by varying the intensity of the outer white ring. Experiments have shown that the color an object appears depends on the intensity and colors of the surrounding area. Perceived colors are not simple functions of objective analysis. Color like contrast as perceived by human vision is highly subjective not objective.

The contrast and color we see in a planetary image is more dependent on our vision than on the real contrast and colors as measured objectively. The perception of contrast and color is largely subjective. They are determined by other properties in the total scene, and not from the objective measurements of the luminance and spectrum. The way human vision processes an image is the single most significant contributor to seeing contrast or color. We often see contrast where no contrast exists and colors that are contrary to the measured spectra. The mechanism, i.e. telescope, that forms and presents the image is not as significant as one would think in producing contrast in an image.

2. Improving Resolution with Very Large Secondaries

Increasing the size of the secondary will increase the resolution of a telescope not decrease it. An obstruction of 99% actually increased the resolution when splitting double stars of similar brightness, (Dall, 1938). This is also discussed in Whysong’s paper, (Whysong, 2004). Splitting double stars of different brightness present other problems. Sirius A and B are an extreme example of the difficulties of splitting doubles of different brightness. In this case the overwhelming brightness of Sirius A makes splitting the two difficult, despite the large angular separation of several minutes of arc.

If you examine the graphs of secondary obstructions in Whysong’s paper it is clear the central peak of the Airy disk gets smaller as the secondary obstruction gets larger. The result is the resolution, in absolute terms, increases. There is also a small shift in the amount of energy from the central peak to adjacent rings in the Airy disk, which is often cited as the reason for loss of resolution and contrast. Despite the small shift in energy, the overall theoretical resolution of the telescope actually increases with increasing secondary size.

3. Airy Disk Energy Distribution

Resolution

The reason often given for decreasing contrast with increasing secondary size is the shift in energy form the central portion of the Airy disk to the surrounding rings. Most of the energy shift is to the first diffraction ring. If you examine the plots provided by Whysong, you will see the central portion of the Airy disk for a 5" refractor is around 1 arc second. With the first ring beyond 1 arc second. A Schmidt Cassegrain with a 34% obstruction shows the central disk is around .75 arc seconds with a little more energy in the first ring which is located under 1 arc second. This means the shifted energy is not observable in 1 arc second seeing or greater. Since typical seeing will limit resolution to more than an arc second the difference is not observable. Given good optics, both telescopes should perform essentially the same given normal seeing, greater than 1 arc second, conditions at the same image scale. There will be a difference in the brightness for the 8" image due to the greater light grasp. If you ever have .75 arc second seeing theory suggests you might see a slight drop in contrast with the 8” Schmidt-Cassegrain as compared to an unobstructed perfect 8” telescope, if the other elements of the telescope including your eye were perfect. However, the absolute resolution will be higher for the 8" Schmidt-Cassegrain.

(Note, the graphs show an 8" Schmidt has higher absolute resolution than a 5" refractor under sub arc second seeing! It is also important to realize the small telescope, 4” and under have inherently lower resolution and contrast than the 8” Schmidt.)

Contrast

If we again examine Whysong’s graphs we see that the shift in brightness to the first diffraction ring is around 10%. Stated another way the change in illumination from the bright central disk to the first ring is around 10%. Recall that contrast is the ability to see differences in illumination. A change of 10% to 30% in illumination is required for the change in brightness, under low light levels, to be perceived by the human eye. [2] A person with very good eyes, on the low edge of this limit, might be able to just detect the shift in illumination, (contrast), caused by secondary obstruction's diffraction under sub-arcsecond seeing conditions. An observer on the high end of this range will not be able to detect the shift in illumination and will not be able to detect the contrast difference. The change in contrast caused by the illumination shift of the secondary obstruction is simply not visible to most observers even under perfect conditions. If we assume the telescopes are under perfect seeing conditions the Schmidt-Cassegrain will still out perform the 5” refractor, in theory, because the shift of illumination to the first ring and the resultant loss in contrast is not visible to the average person. Keep in mind this is for perfect conditions were the eye, aberrations, optics, etc. are all absolutely perfect and the eye is detecting the real luminance of the object, which the eye isn't.

4. Loss of Contrast with High Magnification

High magnification causes a visually observable loss in contrast even with unobstructed telescopes, (Douglass 1897). As the magnification is increased for a given aperture, the image brightness falls off rapidly resulting in a loss of contrast. This would also be consistent with the research by Ratliff discussed in item 1. However, if the background, i.e. sky, can be made darker by the high magnification the perceived contrast may improve, if the loss in luminance is not to great.

5. Seeing

Seeing is the single most important component for high resolution observing, (Douglass, 1897), (Dall, 1938), (Everhart 1959), (Leonard, 2000). Leonard, (2000), reported that contrast suffers more than resolving power under poor seeing condition. This observation should be obvious. It is the number one reason given for lack of high resolution observing in the literature.

6. Other Optical Problems

A litany of other consideration for the degradation of the telescope optical system was also found. They include, dust, scratches, air currents, alignment, optical aberrations, optical coatings, eyepiece quality, eyepiece type, exit pupil, and an undersized secondary can contribute more to loss in contrast than the secondary induced diffraction effects. There are many factors that contribute to the degradation of a telescope image. The contribution due to diffraction caused by the secondary is the least of our worries unless the telescope is being sent into space.

Conclusions

A secondary obstruction does not reduce the contrast of a telescope and resolution increases with increasing secondary size. Unfortunately, most discussions concerning telescope resolution and contrast rely solely on misinterpretations of theoretical results involving perfect telescope optics. Theory does not support claims that secondary obstruction diffraction significantly reduces contrast. Theory does show that resolution is increased. Many factors influence the image quality of a telescope. The effects of other optical components, seeing, magnification, eyepieces, eyeglasses, and how they influence the final image are seldom considered. How human vision effects perceived contrast is not even considered. Despite this, the amateur is fixated on a reported theoretical contrast and resolution loss due to secondary obstruction diffraction based on the interpretation of Airy disk plots. If a loss of contrast due to secondary obstruction diffraction exists, it is small and is usually buried by other imperfections of the total telescope, system including the eyepiece and human vision.

Pursuing the perfect telescope may be fun from a theoretical point of view. From a practical point little will be gained in the pursuit. A professional optical designer, with close to 35 years of optical design and manufacturing experience said,

“Since the computer has been around, more people spend time looking at funny numbers that live inside the computer and never work outside of the box [computer]. Mostly what ifs? I know from optical designing, sure you can design the perfect optical system, but can you build it?”

The whole point of telescope making and amateur astronomy is enjoyment. Amateurs are letting minutia interfere with making and using a telescope. I hope this paper will start to reverse the trend of looking at theoretical numbers and letting insignificant effects dominate telescope discussion and becomes the common knowledge mantra which results in some not making a telescope or reducing the enjoyment of others because their telescope is not perfect. No telescope is perfect. The single most important consideration for an amateur, is the enjoyment of what you view through your telescope. If you enjoy using your telescope, no other considerations are necessary, no matter what an optical design program may say.

References

Whysong, David, 2004, “David Whysong's Calculations of the Airy Disk”, http://www.laughton.com/paul/rfo/obs/diffraction/diffraction.html

Dall, H. E. 1938, “Limitations of Vision With a Telescope” J. Brit. Astr. Assn 48, 163

Douglass, A. E. 1897, “Atmosphere, Telescope and Observer”, Popular Astronomy, June 1897.

Everhart, Edgar, Kantorski Joseph, W. 1959, “ Diffraction Patterns Produced By Obstructions in Reflecting Telescopes of Modest Size”, The Astronomical Journal, December 1959.

Harvey, James E., Ftaclas, Christ, 1995, “Diffraction Effects of Telescopes Secondary Mirror Spiders on Various Image-Quality Criteria”, Applied Optics, Vol 34, No. 28, Oct 1995

Linfoot, E.H., Wolf, E., 1951, “On Telescopic Star Images” MNRAS, Dec. 5, 1951

Ratliff, Floyd, 1972, “Contour and Contrast”, Scientific American, Image, Object, and Illusion, W.H. Freeman and Company, 1974

Wallach, Hans, 1963, “The Perception of Neutral Colors”, Scientific American, Image, Object, and Illusion, W.H. Freeman and Company, 1974

Leonard, Authur S., “Fundamental Limit of Telescope Resolution”, Advanced
Telescope Making Techniques, Volume 1, Willman-Bell 2000.

1 http://www.contrastsensitivity.net/faqs.html
2 http://www.handprint.com/HP/WCL/color1.html

Illustrations

Figures 1-12 “Contour and Contrast”, Scientific American, Image, Object, and Illusion, W.H. Freeman and Company, 1974