|
|
关于MTF，看下面这段：
Factors affecting resolution
In the previous paragraph 7 the theoretical resolution limits of our eyes and binoculars
and telescopes are discussed. However, real life does not proceed via theoretical
limits when using binoculars and telescopes.
The visual resolution is reduced if the observed object has inherently low contrast,
as is the case for most natural objects. Reductions in contrast also occur because
of lightning irregularities, atmospheric effects, diffraction, aberrations in the eye,
focus errors, and effects of misalignments and aberrations in any optical system
employed.
So, the visual resolution using binoculars and telescopes is affected by different
factors, since the image of the natural objects is far more complex than an image
of a point source. The image consists of a multitude of details having different size,
shape, color, brightness, and contrast –a virtually infinite number of bright and less
bright point sources. Each of these contributes a diffraction pattern to the focal
plane, so the final image is the composite of the overlapping diffraction patterns.
In the case of a bright surface and an adjacent dark surface, diffracted light encroaches
into the dark border, causing blurring and unsharpness of the borderline.
A thin dark line on a dark background is “greyed”, while a bright line on a dark
background is widened. These effects are visible particularly when these lines have
an angular width comparable with or smaller than the diffraction pattern. Depending
on the shape, size, brightness, contrast and color of the object observed, the
influence of diffraction on the final image will be different. In that case it is difficult to
find a representative and reproducible method to define the resolution of an optical
system for this kind of image. It was the concept of contrast transfer for optical
systems developed in 1946 by P.M. Duffieux, which yielded considerable insight
into what happens in the image forming process. For details to be visible they
must have sufficient contrast. If the image contrast lies below the eye’s visibility
Figure 42
Intensity profiles across images
formed by the human eye at
different pupil sizes. When the
pupil is constricted in bright light
(pupil size 1,5 mm), the theoretical
diffraction profile (grayed-in
shape) nearly matches the actual
performance profile (area under
thck line) of the eye. At lower
light levels, the eye’s aberrations
increasingly dominate its imaging
capability.
28
threshold, then the detail will be invisible. Image contrast depends not only on the
inherent contrast in the object, but also on how much contrast the optical system
transfers from the object to the image plane. Contrast transfer is the key for understanding
why a certain object detail may be visible in one binocular, but not in
another of the same aperture.
Resolving power and contrast transfer are both quality criteria for every binocular
and telescope. Today it is possible to measure the contrast transfer of an optical
system with special equipment and the relation between image contrast and resolution
can be determined for every point in the image plane with so-called Contrast
Transfer Functions (CTF), the Modulation Transfer Function (MTF) or the Optical
Transfer Function (OTF).
In principle, contrast transfer is measured by placing a grating having a sinusoidal
intensity distribution as an object in front of the optical system, then measuring the
contrast of the resultant image. The ratio between image contrast and object contrast
is called the Contrast Transfer coefficient CT. Each combination of a bright line
and a darker line is called a line pair (lp). A coarse target has a small number of line
pairs per millimeter in the target grating, while a fine target has a high count of line
pairs per millimeter (lp/mm). To evaluate an optical system, we vary the spacing of
line pairs in the grating, and measure the contrast in the image. As the number of
line pairs increases, the optical system renders then with lower and lower contrast
because every point in the object is represented by a diffraction pattern in the
image.
This diffraction pattern scatters light around every image point so that the dark
places in the image are illuminated by diffracted light. This effect becomes more
important as the distance between elements in the image approaches the size
of the diffraction pattern. At some value the image contrast is reduced to zero.
The image of the grating will then be uniformly bright and without any structure.
This is the highest resolving power the system can attain. Duffieux found that the
contrast function for a perfect system is a smoothly decreasing monotonic curve.
CTF curves are extremely useful because we can compare the performance of an
imperfect optical system with the curve for a perfect system. Since the CTF of real
systems is the accumulation of both diffraction effects and various aberrations, we
gain information about the magnitude of image aberrations. The curves for imperfect
systems generally lie below the ideal CTF curve. This means that for the same
resolution, the image contrast of the imperfect system is lower than that of a perfect
system. Image aberrations usually lower the CTF curve more at large numbers
of line pairs per millimeter than at low numbers because the diffraction rings are
brightened at the cost of the Airy disks.
The CTF curve gives a better overall picture of the binoculars’ or telescope’s optical
quality, and certainly yields far more information than testing on double stars possibly
can. It takes into account not only the accumulation of diffraction effects but
also the imperfections in the optical system, not only errors of fabrication but also
of design. The net capability of the binocular or telescope finds its expression in the
position of the contrast transfer curve with respect to the idealized curve. For visual
observation of low contrast details on objects it is difficult to define a meaningful
resolving power for a binocular or telescope. Parameters such as brightness of the
image, intrinsic contrast, image aberrations, and magnification as well as the contrast
sensitivity and visual acuity of the eye must be taken into account. Because of
this, any definition of resolving power is always subject to strict conditions.
29
Because the resolving power for high contrast objects is not sensitive to optical
errors, it is obvious that the common practice of testing telescopes and binoculars
with charts consisting black and white bars is a poor test of optical quality. Conclusions
drawn on the basis of such charts do little to predict the performance of
a binocular or telescope on objects with a low intrinsic contrast. Test charts with
dark grey and light gray lines are more suitable for testing the performance of
these instruments. The Paterson Optical Test Target designed by Geoffrey Crawly,
editor of the British Journal of Photography, may then be an appropriate choice for
resolution tests. It consists of 63 segments (each with structural details of different
shape and ranging from course to very fine) in checkerboard fashion in black, grey
and three colors.
Rutten and Van Venrooij published estimates of the loss of resolving power at different
contrast levels and they came up with the values listed in their table below:
Apart from the above described limitations for determining the resolution of an optical
system one has also to take into account the circumstances that influence the
acuity of the eye and the observation process.
The eye’s resolution at full daylight amounts to approximately 1 minute of arc, but
it decreases with increasing age. The resolution decline starts already from the
age of 20 and at the age of 60 it is diminished by about 25%. That means that a 60
year old eye may have a visual resolution of around 75 arcseconds. The resolution
is also diminished when binoculars are used handheld. Handheld binoculars with
8x magnification may perform 20-30% less due to muscular tremble or shake than
supported binoculars and this difference grows with increasing magnification. This
muscular tremble does affect the visual resolution. |
|
IP卡
狗仔卡
显身卡
