Hadamard Transform Optics by Martin Harwit (Auth.)

By Martin Harwit (Auth.)

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2-15) to hold, the disks must be rotated in such a way that sin θ varies linearly with time, where θ is the angle between the slits and the horizontal. 6 Hadamard Transform Spectrometers Finally, there are the Hadamard transform spectrometers (and imagers), which are the main subject of this book. These are described in detail in the following chapters; for now we just say that they take the form shown in Figs. 3. Chapter 3 The Basic Theory of Hadamard Transform Spectrometers and Imagers If η small objects are weighed in clumps rather than one at a time, the accuracy of the weighings can be increased by a factor of n.

For light returning to the source this would not be true, since one of the beams is reflected twice at the beam splitter, while the other is transmitted twice, and both beams would then be in phase on approaching the source. As one mirror, say M2, is moved while the other remains stationary, the phase relationship between the recombined beams changes as a function of mirror position and of the wavelength of the light. Some wavelengths will reach the detector in phase and reinforce each other while others will interfere destructively and will not produce a signal.

Golay (1961) showed that a necessary condition for a pair of complementary sequences of length ρ to exist is that ρ is even and is the sum of two squares. Thus ρ must be one of 2,4, 8,10,16,18,20, 26,32, 34,36,40, 50, 52, 58,... , are obtained by starting with the pair of length 2 a = 00, b = 01 , and observing that if a and b are complementary so are ab and ab'. 4 Mask Spectrometers 37 Complementary sequences of lengths 10, 20, 40, 80,... and 26, 52, 104,... have also been found, and lengths 18, 34, 36, 50, 58, and 2 x 9 ' are known to be impossible.

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