Probable Object in the Presence of Data

The data im are the measured output spectrum at the exit slit. This is simply the convolution of the number-count object at the entrance slit with the point spread function s(x) of the intervening optics and following electronics, 

The presence of noise in im has been temporarily ignored. Note that the convolution has a discrete form because of the discrete size Ax of the resolution cells in object and image space. Also, it is assumed for simplicity that the form of s(x) does not vary with abscissa xm. 

the object om or nm that satisfies the ML principle (17) must also obey the M constraint equations (18). In addition, there is the normalization constraint (3). These may be tagged onto Eq. (17) by the conventional use of 

Lagrange multipliers. In addition, it turns out to be more convenient to maximize In P instead of P directly. Then the ML principle becomes 

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