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MTF and TDI CIS

I have been recently reading about TDI imagers and their fundamental limitations. A TDI (time delay integration) image sensor effectively performs multiple exposures of the same moving object and accumulates them later on. The aim is to increase the time available for integration of the same object spot and effectively boost the sensor's sensitivity and/or frame rate. Such sensors are typically realized in a large aspect ratio format, normally as line scanners. More about TDIs here.

One very specific and well known issue with TDI imagers is their poor contrast performance. This comes from the fact that when a moving object is captured by static orthogonally placed pixels in e.g. a rolling shutter CMOS image sensor, one can not capture the same object's spots with the same pixels. Here is a diagram of a four-line rolling shutter sensor.

In other words when the rolling shutter is triggered (e.g. left-right), the effective sampling aperture of the sensor depends on the sampling period of the adjacent pixels and the pixel line time. The sampling aperture would therefore affect the dynamic modulation transfer function of the image sensor.Lepage et. al. have an excellent publication in IEEE Transactions on Electron Devices on this problem.

I played numerically with the formulas to see how the number of stages in a TDI sensor would affect its dynamic MTF. The modulation transfer function can be computed by performing a 1D Fourier transform of the sensors' spread function, in the current case due to finite discrete sampling aperture: $$MTF_{discrete} = \frac{\sin(\frac{1}{2}f_{nyq}\pi\frac{t_{int}}{t_{line}})}{\frac{1}{2}f_{nyq}\pi\frac{t_{int}}{t_{line}}}$$ One should also note that the sensor's total MTF would also be affected by the pixel aperture, crosstalk, alignment and is a product of the latter. Below a plot of the dynamic MTF versus the normalised spatial frequency for different effective sampling apertures is shown.

Note at the aliasing peaks beyond the Nyquist frequency indicated with a vertical blue line. We can see that at its best (for a standard orthogonal rolling shutter scanner), if we have a single accummulation the MTF at $f_{n}/2$ is 0.64. As the total MTF of the imager depends also on the pixel's MTF, one can achieve a better total MTF by tweaking the pixel aperture design for e.g. adding some light shields etc... This however degrades pixel QE and therefore gives a loss of SNR.

Date:Tue Nov 6 15:16:56 GMT 2014