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PSF/ MTF Estimation

A point spread function (PSF) or modulation transfer function (MTF) is a measure of how well focused a satellite imaging sensor is.  Every type of camera system has a slight amount of defocus.  Our work in this category is estimating the amount of defocus based on the satellite’s image of specially developed ground targets. 

photo of edge target
edge target
photo of pulse target
pulse target
photo of point target
point target

Three types of targets are used:  edge, pulse, and point targets.  Edge targets and pulse targets consist of placing a highly reflective material next to a very dark material.  These could be tarps spread out on the ground, or level smooth surfaces painted with highly reflective (white) paint and dark (black) paint.  Point targets are sets of mirrors that reflect the sunlight to the sensor.  This light is seen by the sensor as a point source on the ground and the amount of degradation in the sensor’s image of that point source is a direct measure of the PSF for that system. 

 From the image data collected of these targets, calculations are performed to estimate either the PSF or MTF.  The MTF is simply the normalized Fourier Transform of the PSF.  Therefore, when one function is obtained, so is the other.  In general, both the PSF and MTF are functions of two dimensions.  However, the full function is difficult to obtain, so typically only the along-track and cross-track components of the PSF and MTF are furnished to the customer.  Most satellite sensors are specified by meeting certain thresholds on the PSF and/or the MTF such as full width half maximum (FWHM) or MTF at the Nyquist frequency.  Thus, our estimates of these functions, along with these specific measures, allow the customer to determine if his or her satellite is meeting specifications in this category of performance.  An example of the output data produced from this work is shown in Figure 4.

Figure4a, graph of point spread function
Figure 4a

Figure 4a. Example of a Point Spread Function (PSF) for a U.S. sensor in the cross track direction, and including an estimate of the Full Width Half Maximum. 

Figure 4b, photo of satellite image of targets
Figure 4b

Figure 4b. Example satellite image of targets used by the SDSU IP Lab to estimate PSF/MTF.

Figure 4 shows an example of the output obtained from PSF/MTF estimation.  Figure 4a shows the output furnished to the customer.  This is the PSF for a U.S. satellite sensor and represents the amount of blurring in the sensor’s imagery.  Figure 4b shows a satellite image of the types of targets used by the laboratory at its Brookings, SD test site including edge, pulse and point targets.  The plot in Figure 4a was derived from the black/white target in the lower left of the image.