Constraints on digital recording

As has already been mentioned at the beginning of this course, a hologram is a speckle pattern (laser granularity) which corresponds to the interaction between a reference wave and a diffracted object wave, the latter also of “speckle” composition. In terms of zones, the interference fringes generated by two monochromatic plane wave, at an angle of , apart, have an inter-fringe distance (figure 12) of :

The angle imposes almost no constraints in classical holography given the high resolution capability of analogue recording plates. The pixel pitch of current sensors, in digitally acquiring images, is limited. However, their resolution must be sufficiently high in order that the inter-fringe distance corresponds to at least 2 pixels.

The Shannon theorem indicretes that for the correct acquisition of a given periodic signal, the sample frequency must be at least twice as high as the signal frequency. Otherwise, there would be a loss of information due to the weak sampling level. Thus, the first recording condition to be respected is that imposed by the Shannon criteria :

where is the sampling frequency and is the signal frequency which are being studied. Let's consider the case of a digital recording sinusoidal fringes; the sampling frequency corresponds to the inverse of the pitch between two consecutive pixels within the sensor ( or depending on the studied dimension), and the studied signal frequency is the reciprocal of the inter-fringe distance . That is to say :

And

Since the size of the pixels is fixed, the spatial sampling cannot be increased. In order to create good recording conditions, the angle between the object and the reference beams must be adapted.