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25 holography lessons

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24. Adjustment of beams ratio and determination of hologram's exposure time

Adjustment of the optimum ratio of intensities of the reference and signal beams.
The next operation consists in adjustment of the optimum ratio of intensities of the recording beams. This fact reflects advantage of this scheme in comparison with the Denisyuk scheme in which variation of ratio of intensities of the reference and signal beams can be achieved only through changing brightness of the object what isnít always possible. Numerous experiments of recording holograms with the help of the copying scheme have led to some typical values of the ratio between intensities of the reference and signal beams. As a rule the ratio of 1:4 (the reference beam, R, is 4 times more powerful than the signal beam, S, see fig.) is the most universal value. In this case registration of the interference pattern on the hologram occurs on the one hand practically linearly and on the other hand the holographic image is sufficiently bright. This fact is connected with particular features of the light registration by the photographic emulsion. Typical characteristic curve of the photographic emulsion Ė functional dependence of photometric density on exposure is shown in the Fig.1 (black line). The curve shows that by very weak (underexposure) and very strong (over-exposure) exposures functional dependence is nonlinear. The ratio of intensities S:R as 1:4 just allows to locate the integral distribution of illumination values caused by the reference and signal beams on the linear section of the characteristic curve, the sinusoid 1. By the ratio of the beam intensities higher than 1:4 brightness of the hologram decreases without visible improvement of quality. By the ratio of the beams, S:R as 1:1 the image brightness naturally increases but the amplitude of the integral interference pattern drops down to zero at the minima, the sinusoid 2, and because of the nonlinear section of the characteristic curve strong distortions by reproducing details of the object, so called inter-modulation distortions. Itís difficult to get rid of such unfavourable ratio for the beams in the case of objects with highly reflecting surfaces for example by recording images of precious stones or either mirror or well polished surfaces. Light reflects from such objects, which fall on the photoplate develop on the obtained hologram in the form of dark spots, which deteriorate perception of the image and are perceived as defects of the hologram. They can be diminished through increasing the ratio of the beam intensities up to 1:10 and eve higher but then the total brightness of the holographic image will decrease. In other cases itís possible to adjust optimum ratio of intensities of the recording beams practically for any object. For metallic objects or objects covered by colours with metallic components (for example aluminium paint) itís possible to bring the ratio of beams down to 1:3 and for the light reflect even to 1:2 because metallic surfaces donít depolarize radiation and quality of holograms remains high. For nonmetallic objects depolarizing a reflected radiation itís not recommended to decrease the ratio in such a way. For bright objects which have diffuse the light (plaster figures, objects of white paper or cardboard) itís recommended to increase the ratio of the beams up to 1:5 or even 1:6. If there exists a possibility itís better to record a test reflection hologram and already on the basis of it to draw a conclusion about the required ratio of intensities of the recording beams.
Adjustment of the ratio of the beam intensities is carried out by the beam splitter 2 (see second fig. of Lesson 23). Special circular splitters with dielectric sputtering of the reflecting coating are manufactured and for these splitters the reflection coefficient (and correspondingly the transmission factor) changes smoothly depending on the angle of rotation of the splitter. This is the most accurate and convenient way of change of the ratio of intensities of the recording beams. With such a splitter no changes of the trajectories of beams take place and no tuning of the other scheme elements for example the spatial filters which are the devices the most sensitive to displacement of beams is needed. In our arrangement change of the ratio of the beams is based on the other well known principle - dependence of the reflection factor of the dielectric mirror on the incidence angle of the beam. This is not a very convenient method because by changing the inclination angle of the mirror the trajectories of the reflected and transmitted beams change together with variation of the ratio of intensities of these beams and a basic adjustment of the spatial filters should be executed. Nevertheless the result of such work consists in achievement of the optimum ratio for the recording beams in the plane of the hologram and correspondingly good quality of the holographic image. In the fig. the fragment of separation of the beams which includes the beam splitter 2 (numbers correspond to second fig. of Lesson 23), the turn mirror 4 of the reference beam and the spatial filters of the reference (lower) and signal (upper) beams is shown. Measurement of intensities of the beams is carried out with the help of the photodiode in the plane of the photoplate. On the one side of the photoplate (or rather its equivalent Ė a piece of white cardboard inserted into the frame) intensity of the reference beam is measured and on the other side Ė intensity of the signal beam is measured. Measurements can be carried out in relative units because only the ratio of intensities of the reference and signal beams is important for us but they also can be executed in absolute units combining these measurements with the following calculation of the time of exposure of the hologram. Itís important to note that measurements of intensity of the signal beam are carried out in the brightest parts of it. Since such parts can have very small dimensions (for example glare), area of the photosensitive surface of the photodiode shouldnít be very large. In our measurements the photodiode FD-7k having the photosensitive surface with diameter of 3 mm was used (see Lesson 7).

Calculation of exposure time of the reflection hologram.
For calculation of the hologram exposure time illumination of the photographic plate by the reference and signal beams is measured as it was described in the Lesson 7. By the ratio of intensities 1:4 and higher illumination caused by the signal beam can be neglected and the exposure time is calculated only by the level of illumination by the reference beam. But if the ratio of illumination levels in the flashes is 1:3 and less itís necessary to take into account influence of the signal beam and to use total illumination by the reference and signal beams by calculation of exposure otherwise dark spots due to inter-modulation can again appear on the hologram in these places because of inaccuracy of calculations.

References
1. A.L.Kartushanskiy, L.V.Krasniy-Admoni. ďChemistry and physics of photographic processesĒ, Moscow, Chemistry, 1983. -->