Transient phase measurement
using a self-pumped phase conjugate mirror
as an optical novelty filter
M. Esselbach, A. Kiessling, H. Rehn, B. Fleck, R. Kowarschik
A transient phase measuring technique is presented that uses a self-pumped phase conjugate mirror as a novelty filter. A change in the reflectivity of the mirror as a function of a change in the incident wavefront enables the transient measurement of a 2D-phase-distribution. This method allows us to investigate fast processes using media with slow response. A simple theoretical model explains the experimental results with sufficient accuracy. The results can be used for the calibration of the measuring system. The described method is used for the measurement of a temporally varying wavefront.
INTRODUCTION
A novelty filter (NF) is a device that transforms the temporal changes of an input quantity into a measurable output quantity and ignores any static parts. It acts like a temporal high-pass filter. In optics, this means that a change in the spatial amplitude or phase distribution of a signal wave is transformed into a spatial intensity distribution at the output of the device. Known applications of optical novelty filters (ONF), such as motion detection, and edge enhancement, are restricted on qualitative investigations. Phase measuring indeed requires quantitative investigations because the value of a phase change is of interest. That is why this aspect shall be considered in this paper. ONF can be realized by means of the effects appearing in photorefractive media such as barium titanate. The use of the two-wave mixing (TWM), of the beam fanning or of certain interference effects is possible and has been realized. The ONF that will be described and investigated here is based on a self-pumped phase conjugate mirror (SPPCM). It can be shown that the influence of a variation of the signal wavefront on the reflectivity of the mirror can be used to measure transient phase changes.
THEORETICAL STUDIES
In the following, we explain how a temporal change in the phase distribution of the signal wave influences the reflectivity of the mirror. The phase conjugation process can be considered in analogy to real-time holography. A refractive index distribution (grating) is created by the interference of a signal wave and the fanout via the photorefractive effect. This distribution is equivalent to a hologram of the signal wave. The hologram is read out by the reflected fanout. As a condition for this process, the read out wave has to be phase conjugated with respect to the fanout. This is ensured by an self-organizing process during the onset period. However, if the spatial phase distribution of the signal wave changes, the interference pattern (signal wave and fanout) changes too. If this happens in a time period that is short with respect to the response time of the crystal, the refractive index grating remains nearly unchanged. The change of the phase distribution of the signal wave is communicated directly to the fanout and with that to the read out wave. Therefore, the phase distribution of the read out wave changes too. Consequently, the read out condition above-mentioned is no longer fulfilled for the changed parts of the read out wave. Therefore, the diffraction efficiency and with that the reflectivity of the SPPCM decreases. In this way, the change in a phase distribution is transformed into a reflectivity change and finally into a measurable intensity change. But, this simple model does not allow us to derive quantitative results. It is possible to derive an equation for the reflectivity decrease D, where D depends on the phase shift phi. This, on the other hand, offers the possibility to calculate the value of phi from a measured value of D. Thus, it is possible to realize a transient phase measuring technique.The graphs of the function D(phi) are shown in figure 1.
Fig. 1: Theoretical dependence between the relative reflectivity decrease D and the introduced phase shift phi.
EXPERIMENTS AND RESULTS
Following arrangement was used for the measurements.
Fig. 2: Experimental arrangement.
The signal wave is reflected at the SPPCM. The pc wave is coupled out by the semipermeable mirror and falls on the photodetector or on the CCD-camera. The spatially modulated temporal phase change to be measured is introduced into the signal wave by means of an optical addressable liquid-crystal light modulator (OASLM). This device transforms a given intensity distribution on its rear side into a phase distribution of the wave reflected at its front side. It is possible to switch between two wave front forms of the signal wave (with or without changed phase) with the shutter. Now we observed the reflectivity after the introduction of a given phase change into the signal wave for the corresponding part of the reflected beam. Figure 3 shows the result.
Fig. 3: Temporal behavior of the reflectivity of an ESPPCM after the introduction of a phase change into the signal wave.
The reflectivity decreases instantaneously and reaches its initial value again after a certain time. Measurements of the reflectivity decrease as descibed above and with results as shown were carried out for various phase change values.
Fig. 4: Result of the measurement of the dependence between D and phi.
Such a curve can be used as a calibration plot for the practical measurement by assigning the measured value of D to the value of phi. The result of a demonstration can be seen in figure 5.
Fig. 5: Measurement of a given wavefront:
Figure (a) shows the given phase distribution (wavefront) in a 3D representation. The figures (b) and (c) show the two recorded intensity distributions, figure (d) shows the distribution of the calculated D and figure (e) that of the phi. The good correspondence of the figures (a) and (e) implicates that the described method can be practical for phase measurement. An advantage of this measuring technique in comparison with interferometric methods that use a phase shift procedure is, that the camera has to record one picture only during the measuring time. This is of weight especially if the process to be investigated is very fast. Another advantage in comparison with interferometric methods in general is that a reference arm (a separate light path that is not influenced by the phase object) is not needed. The measuring device is connected in series to the phase object to be measured. So the influence of vibrations of the arrangement etc. on the measuring process can be reduced.
The maximum speed of a process to be investigated with the described method is only limited by the camera and not by the optical part of the arrangement. That is why this method is suitable for the investigation of fast processes.