On Some Properties of Photographically Produced Diffraction Gratings A. K. Rigler and T. P. Vogl

Westinghouse Electric Corporation, Research and Develop­ment Center, Pittsburgh, Pennsylvania 15235. Received 23 February 1966. Presented to the Optical Society of America, 18 March 1966, Paper FH16.

Holograms have frequently been described as modulated diffraction gratings. Therefore, i t is of interest to study the diffractive properties of such gratings. The idea of a photograph­ically produced diffraction grating is certainly not new.1'2 How­ever, the great coherence of a laser light source permits results previously impossible.

We have made several gratings using the configuration de­picted in Fig. 1. In Figs. 1 and 2 our notation follows that or Born and Wolf.3 The recording and observation wavelengths are denoted by λr and λ0, respectively. The anticipated line spacing is derived as follows: two beams of approximately equal intensity strike the emulsion surface at the same angle of incidence α. The spacing d between density maxima in the developed emulsion is given by d = λ /2 sinα , where α is the angle between the beam

1086 APPLIED OPTICS / Vol. 5, No. 6 / June 1966

Table I. Comparison of Predicted and Observed Grating Performance

Fig. 1. Configura­tion of the record­

ing apparatus.

Fig. 2. Illustra­tion of dispersion

measurement.

and the surface normal inside the emulsion and λ is the wave­length inside the emulsion. In terms of the external angle of incidence and wavelength

These gratings were made using an He-Ne laser; λr = 0.6328 μ. With the values of d predicted by Eq. (1) and using the laser as

a source, we search for the possible orders m as given by

where the angles θm and θ0 are defined in Fig. 2. Only the first order was detected and when the grating was adjusted for equal angles of incidence and diffraction, the intensity of the diffracted beam was maximum as expected.4 About 10% of the transmitted light appeared in the diffracted beam.

From the dispersion equation

and Eqs. (1) and (2) above, we predict the angular dispersion of these gratings:

We verify this prediction by measuring the dispersion of the 0.5770-0.5791 μ doublet of a mercury source. The measurements were taken with a crude spectrograph assembled from two half-meter focal length parabolas which yielded the spectra shown in Fig. 3. The grating was adjusted for maximum intensity in the diffracted beam. Experimental values for d were obtained from Eq. (2). The results are shown in Table I.

These preliminary results indicate that relatively high disper­sion gratings with reasonable efficiency can be easily produced photographically. Our measurements were obtained using the grating in transmission. As expected,5,6 these properties have also been observed in reflection from the emulsion surfaces.

Fig. 3. Composite photograph of recorded spectra of the Hg doublet in order of increasing α in the table. Photographs were taken without an exit slit using the half-meter instrument mentioned in the text. The insert scale is 1 cm. Note the

presence of the 4561 °-μ line in the lowest dispersion spectra.

We gratefully acknowledge instructive conversations with J . W. Coltman and the assistance of E. P . Supertzi in obtaining the data.

References 1. K. V. Krishna Rao, Am. J. Phys. 30, 106 (1962). 2. Yu. N . Densiyuk, Opt. Spectry. 15, 279 (1963). 3. M. Born and E. Wolf, Principles of Optics (Pergamon Press,

Inc., New York, 1964). 4. Lord Rayleigh, Scientific Papers (Dover Publications, Inc.,

New York, 1964), Vol. 3, p . 117. 5. T. P . Vogl and A. K. Rigler, J. Opt. Soc. Am. 55, 1566

(1965)—abstract. 6. A. K. Rigler, J. Opt. Soc. Am. 55, .1693 (1965).

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