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Chapter 17:
MTF, Limits, and Pixel Sizes
Author(s): Max J. Riedl
Published: 2009
DOI: 10.1117/3.835815.ch17
17.1 Introduction The optical modulation transfer function (MTF) is a well-known concept for evaluating the performance of a lens. It contains valuable information about the resolving power of the lens and the contrast in the image. Modern infrared imaging systems use sensor arrays that are made up of small individual sensing elements, the pixels. The practical minimum size of such a pixel depends on the wavelength of the collected radiation and sets the spatial resolution limit of the optical system, referred to as the Nyquist frequency. 17.2 Optical Modulation Transfer Function The MTF for diffraction limited systems is expressed by MTF diffr (v)=2 π [arccos(v v 0 )−(v v 0 )1−(v v 0 ) 2 − − − − − − − √ ], where v is the spatial frequency of interest, v 0 is the cut-off frequency, and v∕v 0 is the normalized frequency. Figure 17.1 shows the graph of the diffraction-limited MTF as a function of the normalized frequency v∕v 0 . In Fig. 17.1 there is also a remark about the Nyquist frequency, which will be discussed in the following section. The cut-off frequency is expressed by v 0 =1 λ(f∕#) This indicates that for the visible spectrum with λ=0.5μm, the cut-off frequency in line pair/mm v 0 VIS =2000∕(f∕#). In the MWIR region, with λ=4μm, v 0 MWIR =250∕(f∕#). For the LWIR spectrum, with λ=10μm, v 0 LWIR =100∕(f∕#). These numbers are reminders of the sizeable differences among the different spectral regions.
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Modulation transfer functions

Long wavelength infrared


Staring arrays

Spatial frequencies

Image sensors

Imaging systems

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