Many optical sensing and measurement techniques are known that are based on temporally modulated optical radiation fields whose local amplitude and phase vary as a function of time. These techniques require the spatially and temporally resolved determination of amplitude and phase, the so-called demodulation of the modulated radiation field. While several electronic circuits and digital signal processing algorithms exist that can provide this demodulation function for a single measurement spot, none of these solutions allow the integration into dense, massively parallel and reliably operating arrays of demodulation photosensors.
A standard AM-demodulation consists of band-pass filtering, rectifying, and low-pass filtering the input signal. This technique is widely known for AM radio receivers. Its disadvantage is the need for large RC-constants for frequencies below 10 kHz, which are not compatible with the small pixel size and the new CMOS processes.
Direct detection by multiplying the input signal on one path with an oscillator signal matching the carrier frequency and on a second path with the oscillator's 90-degrees shifted signal allows detection of amplitude and phase. But signal multiplication is complex and power consuming compared to the power available in each pixel (typically a few μW) and therefore not suited for massive parallel integration in a pixel field.
Several digital demodulation techniques are known based on oversampling the input signal. Due to the Nyquist Sampling theorem, the sampling rate must be more than twice the input-signal bandwidth. Digital signal demodulation algorithms are normally too complex to be implemented into a pixel (more than 50 transistors). The following non-exhaustive list gives an overview of digital demodulation techniques:                A widely used method applies a discrete Fourier transform, removes negative and zero frequency components and re-centers the spectrum before reverse transforming. This method is described in S. S. C. Chim and G. S. Kino, “Correlation microscope,” Opt. Lett. 15, pp. 579-581, 1990.        If the input signal is sampled at a frequency that is four times the input signal modulation frequency, different algorithms for local envelope detection are known. An evaluation can be found in K. G. Larkin, “Efficient nonlinear algorithm for envelope detection in white light interferometry,” J. Opt. Soc. Am. 13, pp. 832-843, 1996. But all of them imply multiplication and are therefore not applicable in a power efficient pixel structure.        
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