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WHITE PAPER
How to Include Detector Resolution in
MTF Calculations
Zemax
A Radiant Zemax Company
WHITE PAPER
How to Include Detector Resolution in
MTF Calculations
Introduction
Modulation Transfer Function (MTF) is an important method of describing the performance
of an optical system. A consequence of applying Fourier theory to image forming optical
MTF is commonly used to describe the
systems, MTF describes the contrast in the image of a spatial frequency presented in the
performance of an imaging system, but
scene being viewed. See this article for more information on what MTF is.
the finite resolution of the detection
system is often ignored. This white
MTF describes the imaging of the system, but an important system parameter is usually
paper describes how to account for
neglected: the resolution of the detector. If the detector’s pixels are significantly bigger
detector pixel sizes and position shifts
than the resolvable spot size, the optical system is said to be detector limited, and the
to give a full-system MTF measurement.
overall system MTF is reduced compared to the MTF the optical system itself is capable
of achieving.
Experimentally, MTF can be measured by imaging a small bar (or single-frequency sine)
chart through the lens and onto the detector. The bar chart must be small because the
optical transfer function of the lens should not vary significantly over the target pattern.
Within Zemax we can use the same method: the partially coherent image analysis
feature is used to image a small bar chart through the system onto a pixellated detector,
and the MTF is computed directly from this.
An Example
The example file used here can be downloaded via this link. It is a derivative of the
Cooke triplet sample file:
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We image a bar chart through the system:
The full width of the image is 0.5 mm, and the optical performance of the lens does not vary
significantly over this field of view:
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We will now look at the cross-section of the Partially Coherent Image Analysis,
configured like so:
so we use 500 1µ-wide pixels to view our image. The resulting image is like so:
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The cross section of the false color map is shown above. Note we have ten cycles of
the bar pattern over about a 200µ region: this corresponds to 50 cycles/mm. The MTF
can then be estimated by determining the maximum and minimum relative intensity
across the cross section.
To reduce the effects of edges, the analysis parameters should be set to provide at least
5 well defined peaks across the cross section. The MTF is computed by looking for the
minimum and maximum intensity at all points between the second and second-to-last
local peaks in the intensity data. By considering only data within these two peaks, the
effects of the edges is somewhat reduced.
The estimated MTF is then given by the usual computation of (Imax-Imin)/(Imax+Imin).
Finally, note that if a bar target is used, the resulting MTF is the square-wave, not sinewave modulation:
Note there is excellent agreement between the two analysis features, with an estimated
MTF of 0.68 from both the Partially Coherent Image Analysis and the FFT MTF plot at
50 cycles/mm (note that we are only approximately at 50 cycles/mm in the Partially
Coherent Image Analysis). This is to be expected, as the 1µ detector pixel size is smaller
than the 5µ RMS spot size and 3.5µ Airy disk radius. This combination of optical system
and detector is optics limited, not detector limited.
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Instead, repeat the Partially Coherent Image Analysis, but use an array of 100 x 100
pixels each of 5µ width. Now the MTF is 0.43:
The MTF is clearly degraded by the coarser detector resolution. Equally important,
consider what happens if the detector is shifted in the image plane. Because the pixel
size is close to the resolution limit, the measured MTF will be sensitive to shifts of the
detector array on the order of one pixel. If we decenter the detector by a half-pixel in x...
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...the MTF improves to 0.59 because there is less cross-talk between light and dark
regions of the image as they are integrated by the detector array:
Summary
If an optical system’s minimum resolvable spot is comparable to or less than the
detector size, it is important to consider the effects of integrating the spatial signal on
the detector array when computing MTF. The Partially Coherent Image Analysis feature
provides this capability.
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MTF is commonly used to describe the performance of an imaging system,
but the finite resolution of the detection system is often ignored. This white
paper describes how to account for detector pixel sizes and position shifts
to give a full-system MTF measurement.
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