Wide-Angle Narrow-Band Interference Filter Photography G. T. Best and C. A. Forsberg

Air Force Cambridge Research Laboratories, Bedford, Massachusetts 01730. Received 21 October 1972.

Interference filters are frequently used to improve the photographic contrast of images of phenomena such as au-rorae1 or high altitude chemical vapor releases2 where the spectral radiation of the feature of interest is limited to a narrow wavelength region. The conventional technique is to place the filter in front of the camera lens, in which case the spatial extent of the photographic coverage is de­termined by the angular field of the camera. The con­trast is improved by using filters of narrower bandwidth, but as the filter used is made more narrow, its transmis­sion properties become more sensitive functions of the angle θ between the incoming rays and the filter normal. The most serious change is . the shift to shorter wave­lengths of the transmission peak, given by3

where μe is the effective refractive index of the spacer layer. This approximation is valid for values of θ less than 20°. The effective angular field is maximized for a given wavelength and bandwidth by designing the filter for a longer wavelength so the half-power point for the re­quired wavelength occurs on axis. The semiangular field then extends out to the other half-power point, and the solid angular field of the filter given by

This is clearly recognizable as a variant of the Jacquinot criterion4

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where Ω is the solid angular field over which a spectral resolution R can be maintained. A convenient rule is the fact that at 6566 Å, the semiangle in degrees, when deter­mined by Eq. (3) is numerically equal to the square root of the bandwidth in angstroms. Hence where narrow band filters are used, it is not normally possible to form images over a wide field angle and still maintain the re­quired monochromaticity. Some techniques for overcom­ing this problem, using auroral all-sky cameras, have been described by Hunten.5 In the instruments described, at least four lenses are required in addition to the all-sky camera mirror.

In preparing instrumentation for the observation of E region barium releases at twilight,6 it became necessary to devise a means of achieving a moderate field angle (about 10°-20°) with a narrow-band filter (2.5 Å) centered at 4934 Å. This was required to detect optically any barium ion cloud that might be formed, an intense background being expected due to the necessarily low solar depression angle and the anticipated dense cloud of barium oxide that has fluorescence bands throughout the visible. Two simple optical systems were designed for this purpose; and, since the slightly more complex (and flexible) system leads logi­cally to the simplest (which was in fact used), it will be described first.

Suppose we take a lens and place a pinhole aperture at the front focus. An image of the sky will be formed on the lens; and if an interference filter is placed behind the lens, it will be illuminated by perfectly collimated light. A second lens placed some distance behind the filter can now image the field lens (and the sky) on the final focal plane. Obviously, the pinhole can be replaced by a small lens of sufficient aperture to use the full solid angle of the filter. Clearly the angular field is determined by the F-number of the field lens, and if unity magnification is produced by the final lens, the effective F-number of the system is just that of the first lens, given by F = (λ/8 AX)1/2. The flexibility of this system arises from the fact

Fig. 1. Densitometer scans of images of the sky and a monochro­matic radiance source showing the improvements obtained using the

telecentric system.

that, if the third lens is used to form a reduced image, the effective F-number of the system is reduced proportion­ately. Since a 2.5-Å filter permits illumination by an F/16 beam, and the filter may be made as large as 50 mm diameter, clearly a reduction of F-number and image di­ameter would permit brighter images to be formed on conventional sensors (e.g., 25-mm Vidicon).

Analysis of the three-lens system shows that, for the special case where the final image is in fact formed at the rear focus of the field lens, the focal lengths of the first and third lenses become infinite, i.e., they are replaced by simple apertures. This is the well-known case of the tele-centric stop and has the advantage that neither the lens nor the filter (with their small defects) is near an image plane.

This type of system was constructed using a Zeiss Bio-tar lens of focal length 75 mm and relative aperture F/1.5. Tests were carried out by photographing the sky back­ground alone and separately a monochromatic radiance source (barium hollow cathode lamp with diffuser), the latter being positioned successively at a series of angles to the principal axis to investigate the angular variation of sensitivity to monochromatic radiation. The results of these exposures, as densitometer scans along a diameter of the image, are shown in Fig. 1 for both the normal and the improved filter camera using a 2.5-Å filter in both cases. The Fraunhofer absorption features identified in Fig. 1 appear as concentric rings and display the shift of peak transmission to shorter wavelength with increasing angle, which is characteristic of interference filters. On the other hand, the sky background obtained with the modified filter camera shows only the gradient of the sky radiance itself. The lower portion of the figure shows the improved uniformity of response to monochromatic radia­tion.

One difficulty with the telecentric system is that for wide angular fields, since the angular field is 2 arctan (1/ 2F), a lens of low F number is required. These frequently

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have the front focus so close to the front element that there is no room for the interference filter. Since this lens configuration requires only the correction of spherical aberrations and not chromatic aberration, it should be possible to design simpler lenses for which this difficulty does not arise. It is also noted that this limitation does not apply to the three-lens system. Finally it should be noted that, since the image is illuminated at normal inci­dence by a small relative aperture, it is ideally suited for coupling to image intensifiers with fiber optics face plates. The use of intensifiers is desirable because of the loss in relative aperture accompanying the increased angular field.

References 1. R. H. Eather and D. L. Reasoner, Appl. Opt. 8, 227 (1969). 2. N. W. Rosenberg, Science, 152, 1017 (1966). 3. J. Ring, in Astronomical Optics and Related Subjects, Z.

Kopal, Ed. (North-Holland, Amsterdam, 1956), p. 381; P. H. Lissberger and W. L. Wilcock; J. Opt. Soc. Am. 49, 126 (1959).

4. P. Jacquinot, J. Opt. Soc. Am. 44, 761 (1956). 5. D. M. Hunten, Scientific Report No BR-21, University of Sas­

katchewan, September 1959. 6. N. W. Rosenberg and G. T. Best, J. Phys. Chem. 75, 1412

(1971).

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