Diffraction efficiency

For the reflection geometry shown in Figure 6b, the diffraction efficiency is given by equation 13. 

For both geometries the diffraction efficiency approaches unity in value for Atransmission hologram exhibiting a periodic behavior (24,25) efficiency as a function of the grating strength ( ), whereas the reflection efficiency exponentially approaches unity. 

Materials Spectral range, nm Resolution, lines / mm Exposure required, lj/cm Diffraction efficiency, % Reusabihty ... 

Fig. 3.2. X-ray diffraction efficiency of the (111) reflection of Bi after excitation with an optical pulse at 6mJ/cm2. Circles and solid curves are the experimental data and the fit, respectively. From [2]...

Dichromated gelatin. This material is particularly sensitive to light in the blue and UV regions, but not the red. They are used to produce volume holograms that approach the theoretical limit in diffraction efficiencies. 

Figure 7.9 Diffraction efficiency versus energy density for pure amorphous selenium in the low-energy-density region. The lines are eye-guides.

Figure 7.10 A change of diffraction efficiency in a-Sb Sei samples induced by laser irradiation. X = 0 and 0.03 in curves 1 and 2, respectively. Thickness is 1.25 pm and I = 1.25W/cm. ...

As in the case of photoanodic etching, a certain optimal time exists here, during which the etched relief attains the most regular shape a maximum value of diffraction efficiency corresponds to this time. 

Fig. 33. Diffraction efficiency versus voltages for spatial frequencies in mm-1 10 (/), 28 (2), 51 (i). Switch on time versus voltages at spatial frequencies in mm"110 (/ ), 36 (2 ), 60 (S ). Commutational regime for polyimide-liquid crystal modulator with controlled birefringence [256]...

Fig. 34. Diffraction efficiency versus spatial frequency for electrically controlled birefrigence liquid crystal-polyimide modulator in pulse regime [257]...

Photochemical methods for hologram recording are very similar to the ones mentioned above. Excellent holographic parameters were obtained for polydiacetylenes [173, 174]. A diffraction efficiency of up to 40% for a spatial frequency of 1600 mm 1 and with a sensitivity of 5 cm2 J-1 was realized. Such a medium may be used in optical processing. 

For the moment, it is sufficient to know that the sample response, which is the time dependent diffraction efficiency after switching off the optical grating, contains at least a fast contribution from heat and a slow one from mass diffusion. The corresponding diffusion time constants depend on the grating constant and are typically of the order of 10 /rs and 100 ms, respectively. 

Xr is the readout wavelength and s the sample thickness. Q < 1 indicates thin, Q > 1 thick grating conditions,which are prevalent in the present case with Q 5. An extensive treatment of the diffraction theory of phase gratings has been given by Kogelnik [48]. All experiments discussed here have been conducted within the weak modulation depth limit, where the heterodyne or electric field diffraction efficiency Chet(t) is simply proportional to the refractive index modulation depth ... 

Chet(t) can be complex to account for phase shifts. The homodyne diffraction efficiency, which is measured in the absence of coherent background, is proportional to nq(t) 2. 

Now, all steps can be combined to calculate the heterodyne diffraction efficiency from Eqs. 9,16,20,21, and 23. After normalization to the diffraction efficiency of the steady state amplitude of the temperature grating, one arrives at... 

Equation (25) holds for monodisperse samples with a single diffusion time constant t, and the diffraction efficiency in response to the most fundamental excitation, a step function where the grating amplitude is switched from 0 to 1 at f = 0, is [27,28,35,45]... 

Fig. 9. Normalized heterodyne diffraction efficiency for toluene/n-hexane (toluene weight fraction 0.517) and ethanol/water (ethanol weight fraction 0.391). From Ref. [49]...

In this section it will be outlined how the different molar masses contribute to the TDFRS signal. Of especial interest is the possibility of selective excitation and the preparation of different nonequilibrium states, which allows for a tuning of the relative statistical weights in the way a TDFRS experiment is conducted. Especially when compared to PCS, whose electric field autocorrelation function g t) strongly overestimates high molar mass contributions, a much more uniform contribution of the different molar masses to the heterodyne TDFRS diffraction efficiency t) is found. This will allow for the measurement of small... 

Fig. 20. Normalized heterodyne diffraction efficiencies for a concentration series of 1 20 crosslinked PS microgels in toluene. The insert shows the rate distribution for the lowest concentration, corresponding to the slowest decay curve. From Ref. [64]...

Now, the effective linear response function h(t) can be identified with g(t) as defined in Eqs. (25) and (29) h(t) = g(t). The primary sample response is the heterodyne diffraction efficiencyy (t) = Chet(t)- The instantaneous contribution of the temperature grating to the diffraction efficiency is expressed by the 5-function in g(t) [Eq. (25)]. After the sample, an unavoidable noise term e(t) is added. The continuous yff) is sampled by integrating with an ideal detector over time intervals At to finally obtain the time-discrete sequence y[n]. 

The lower half of the insert shows the heterodyne diffraction efficiency as seen by the detector. It has a random character, but the influence of the memory function is obvious when compared to the excitation. The main part of Fig. 26 shows the concentration part of the memory function g(t) h(t) after deconvolution according to Eq. (61). The amplitude of the contribution from the temperature grating is normalized to unity and contributes only to the very first data point. 

We have outlined how TDFRS not only provides a useful tool for the study of the Ludwig-Soret effect in multicomponent liquids, but can also contribute valuable pieces of information towards solving the puzzles encountered in polymer analysis. Though TDFRS is conceptually simple, real experiments can be rather elaborate because of the relatively low diffraction efficiencies, which require repetitive exposures and a reliable homodyne/heterodyne signal separation. As an optical scattering technique it has much in common with PCS, and the diffusion coefficients obtained in the hydrodynamic limit (q —> 0) for monodisperse solutions are indeed identical. 

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