Long optical paths of large aperture
THE measurement of the vapor phase spectra of compounds having high boiling points presents an experimental problem that may be solved either by heating the absorption cells or by making them very long. In the infra-red region radiation from the hot gases in heated cells decreases the accuracy of absorption measurements. If only a small amount of sample is available, the only possibility is to use an optical system in which the radiation goes back and forth through the same volume a large number of times. Several designs for such systems have been published recently1, 2 but none of them permits the use of large angular apertures at points off the optic axis. In this paper an absorption cell is described in which the light traverses a small volume a large and arbitrarily variable number of times, and in which the angular aperture of the mirrors is not occulted either on or off the optical axis. The design gives very high light transmission and can be used for observing spectra that are very weak, or that belong to high boiling point compounds or to compounds obtainable only in very low concentrations. It can be used for any liquids or gases that do not injure the mirror surfaces, with which they are directly in contact.
The essential parts of the equipment are three spherical, concave mirrors that all have the same radius of curvature. These are set up as shown in Fig. 1 with two mirrors A and A’ close together at one end of the absorption cell, and the third mirror B at the other end. The centers of curvature of A and A’ are on the front surface of B, and the center of curvature of B is halfway between A and A’. This arrangement establishes a system of conjugate foci on the reflecting surfaces of the mirrors, by which all the light leaving any point on A is brought to a focus by B at the corresponding point on A’, and all the light leaving this point on A’ is focused back again to the original point on A. Similarly, all the light leaving any point on B and going to either A or A’ is focused back to a new point on B that is somewhat offset to one side of the original one.
Figure 1 illustrates the way these properties are used to obtain very long optical paths. Light enters through a slit close to one end of B, whence it goes to A, from there to B, then to A’, back to B, to A, and so on, back and forth between B and A’ or A alternately. The positions of successive images can all be located by the rule that object and image points near the center of curvature of a spherical mirror always lie on a straight line whose midpoint falls on the center of curvature. Thus mirror A forms an image 1 of the entrance slit on the surface of B as far from A’s center of curvature as the entrance slit is from it. Then, since the center of curvature of mirror B, shown by a circle, is halfway between A and A’, B forms an image of A on A’. In the same way, mirror A’ forms on B a second image 2 of the slit, whose position is determined by the distance between 1 and the center of curvature of A’. Mirror B forms an image of A’ on A, and A forms another image 3 of the slit on B, which is again returned to A, and so on. Each successive image of the slit on B is offset to one side or the other of the preceding one until finally the last one falls beyond the end of B. The different images fall in order at the points marked 1, 2, 3, and 4 in Fig. 1. The large angular aperture obtainable off the optic axis is easily explained. Since all the light in the first image of the slit that is formed on B is focused on A’, and since all the light failing on A’ is returned to the second image on B, and so on, no light is lost off the edges of the mirrors. The only way intensity can be lost is by absorption or scattering on the reflecting surfaces.
The optical adjustments of this system are not critical; most of the tests and photographs described here were made manually without screw adjustments. The most important adjustment is the separation of the centers of curvature of the mirrors A and A’. This determines the number of times the light goes through the cell and the uniformity of the separation of the images formed on B. If A and A’ are adjusted symmetrically about B and its center of curvature, each image on B is separated from the ones nearest to it by the distance between the centers of curvature of A and A’. The ratio of the length of B to this separation determines the number of times the light passes through the cell. This may be either four times for one image on B, eight times for three images, twelve for five, sixteen for seven, etc. Intermediate numbers are not possible. If A and A’ are not symmetrically adjusted horizontally, the images on B occur in pairs rather than uniformly spaced. If A or A’ is out of adjustment in the vertical rather than the horizontal angle, alternate images are raised or lowered above the others. In neither case is there any loss of intensity or troublesome cumulative effect of the error. If B is out of adjustment either horizontally or vertically, the first image of A does not fall exactly on A’, and some light is lost around its edges. However, after one reflection there is no further loss, because that part of the light which did fall on A’ is reflected back and forth between the same points on A and A’.