Glossary
MTF (Modulation Transfer Function) is a contrast characteristic for each spatial frequency that expresses how the repetition of shading on the object's surface is reproduced on the image side in terms of spatial frequency and contrast ratio. Simply put, MTF expresses the imaging performance of a lens and how faithfully it reproduces the contrast of an object as an image. Contrast is the difference between light and dark at a given resolution (frequency) on an object. In the case of the black and white square wave shown in Figure 4, the contrast ratio for black and white is 100%. This pattern is captured by the lens and the contrast ratio on the lens image plane is quantified. Object Figure 4 This is used with respect to lens imaging characteristics as an indicator of resolving power. It expresses the decrease in contrast when a subject is projected via a lens onto an image surface in terms of the spatial frequency and the contrast ratio. (Refer MTF and Resolution )
MTF （Modulation Transfer Function）
Phenomenon in which the edges of an image are compressed inward, causing the center of the image to appear swollen (barrel distortion) or in which the edges of the image are expanded outward, causing the center of the image to appear drawn into the center of the image (pincushion distortion).
Figure 1
Figure 2
Ideal Object Actual Object
Distortion
Barrel distortion
Pincushion distortion
Basically, the contrast ratio gradually decreases when a pattern with a fine frequency is imaged than when a pattern with a rough frequency is imaged with any lens, because the influence of optical aberration etc. is greater. When the contrast ratio is finally reduced to 0%, the white pattern and the black pattern are both gray and completely indistinguishable.
y’ ×100
TV.D= △h ×100 2h
D= y’－ y’
A percentage value indicating the degree of curvature of straight lines in the direction of the long side of the imaging element.
TV.Distortion
White
Figures 5 and 6 show the change in spatial frequency between the object and the image side. The horizontal axis of the graph is the spatial frequency and the vertical axis is the brightness. The contrast between the object side and the image side at a certain frequency can be calculated by the formulas in Figures 5 and 6 as A and B 100% Contrast Black
Relationship between principal points and image formation: Optical Magnification is the ratio between the size of an object and the size of an image. the relationship is as follows.
H
H'
Figure 3
y
NA
NA' y'
Object side
Image side
Optical Magnification
Figure 5
Figure 6
H = Front principal point H'= Rear principal point
a
a'
Opt.Mag(M)= = = y' y a' a
NA' NA
lmax
Opt.Mag(M)= effective camera sensor size (V) or (H) FOV (V) or (H)
lmax
l max
l max
l min
TV Monitor Magnification is the magnification on a monitor when an object is imaged by camera and is displayed on the TV monitor.
l min
MTF and Resolution
lmin
lmin
High
High
Low
Low
B ＝ lmax - lmin lmax + lmin Spatial Frequency(ν)
Spatial Frequency(ν) A ＝ lmax - lmin lmax + lmin
Monitor diagonal Camera sensor diagonal
Sensor
×Optical Mag.＝Monitor Mag.
Camera
[Formula and calculation example] with 1/2” CCD , monitor the image using VS-MS1+10x objective lens on a 14 inch monitor. The magnification on TV monitor will be
sensor diagonal
Figure 7 As mentioned above, since contrast is normally reproduced faithfully at low frequencies, the MTF is close to 100% and contrast at high frequencies becomes indistinct, and therefore the image becomes gray and indistinguishable beyond the limiting resolution frequency. In reality, aberration in the lens causes the contrast to be lost before the critical resolution is reached. Generally speaking, the threshold is 0.1. If you look at Figure 7 with this in mind, you can see the following. In general, the quality of a lens is often judged by its resolution value, but in fact, both MTF and resolution are highly relevant. The figure below illustrates the relationship between resolution and MTF. The figure shows the MTF curves for two lenses with different performance. Lens (a) has a low critical resolution but high contrast performance at low spatial frequency, while lens (b) has a high critical resolution and low contrast performance at low spatial frequency.
TV Monitor Magnification
25.4×14（inch） 8（mm）
×10(x)＝444.5x
Therefore, a 0.1mm scale will appear on the monitor at 44.45mm. *Please use the above calculation as a guideline while it may change slightly when the TV monitor is on Overscan mode.
objective lens
Monitor
The magnification rate of an image shown on a TV monitor with respect to the image being shown is expressed using the following formula. (Optical magnification) x (TV monitor magnification) The expression is a line pair (lp)/mm and shows how many black and white line pairs can be seen within 1 mm.This indicates the theoretical limit of recognizable distances between two points. 0.61 x wavelength (λ)/N.A. = theoretical resolution (μ). The above formula gives the theoretical resolution. However, optical aberration is not included. * The wavelength used is calculated at 550 nm The number of line pairs that can be resolved close together at a constant pitch. This is often expressed in terms of resolving power. (Object space resolving power) = (Image space resolving power) x (Optical magnification)
A B
MTF M（ν）＝ ̶
When verifying in the low frequency region around I described in the MTF graph, lens a is better, and when verifying in the high frequency region around II, lens b is better. From the above, it seems that lens b, which has a good basic performance (limit resolution), is the better lens, but in the end it depends on the usage environment of the person who uses it, and is difficult to judge the quality of the lens based on resolution alone.
MTF
100%
Lens a
Lens b
Resolution
50%
Threshold
0%
Ⅰ
Resolution limit of "a"
Resolution limit of "b"
Ⅱ
Resolving Power
Low
Spatial Frequency
High
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