The radial distribution of energy within an image, called encircled energy, is a classical measure of the quality of the optical system producing that image. An improved method for measuring encircled or enclosed energy for imaging optical systems makes use of precisely micromachined apertures which are positioned with great accuracy at the center of an image.

The technique is an improved solution to the problem of measuring radiant fluxes passing through a sequence of round or square holes of progressively increasing size, all centered on the same point of interest in a focal plane of the optical system. The sequence of measurements determines the radial distribution of irradiance about the point of interest. This distribution is useful for specifying and characterizing the performance of the optical system; in particular, if the point of interest is the nominal center of the image of a bright point object, then the desired distribution is related in a known way to the point-spread function of the system.

The concept of using progressively wider apertures of identical shape to measure the radial distribution of irradiance is so straightforward as to seem almost trivial; however, in practice, it has historically proven difficult to implement this concept with the precision needed to characterize the performances of advanced vacuum-ultraviolet and x-ray imaging instruments. The difficulty lies in being able to interchange each aperture exactly concentrically and in focus, especially with a collection of discrete apertures. Alternative methods which involve knife-edge or slit scanning are always indirect approaches to measuring encircled energy and produce somewhat ambiguous results.

The new method affords all of the necessary precision. An opaque mask containing a linear array of identically-shaped but differently-sized apertures has been fabricated by chemical micromachining in a thin, flat silicon substrate. Also fabricated during the micromachining process are a set of binary-coded fiducial marks - one mark for each aperture, located at a known distance well to the side of the aperture. The precision of dimensions and locations of apertures and fiducial marks are of the order of 0.1 to 0.2 µm - commensurate with the state of the art of microlithography. Aperture sizes pro-gress slowly from 1 µm all the way up to 2 mm in both circular and square aperture shapes.

The aperture mask is mounted in front of a photodetector on a translation stage with three mutually orthogonal axes with 0.1-µm position resolution - one for motion perpendicular to the focal plane (focus) and two for motion within the focal plane.

The linear array of apertures is carefully mounted so as to be parallel to the direction of travel of one of the latter motions. The exact position of the selected aperture of interest in the focal plane is sensed by using an optoelectronic apparatus to measure the position of the associated fiducial mark: A lens focuses a magnified image of the backlit fiducial mark onto a small charge-coupled-device (CCD) image detector. The CCD output is digitized and processed to decode the binary pattern (and thereby the selected aperture) and to determine the position of the aperture to within about 0.01 µm.

In preparation for the measurement process, a photodetector wider than the focal spot of interest is positioned just behind the focal plane to intercept the focused light. The largest aperture in the aperture mask is centered approximately on the image, then moved from side to side along both image-plane axes while observing the photodetector output to find the points, corresponding to passage of the aperture edge, beyond which the light is totally blocked. The center of the image is tentatively deemed to lie halfway between the extinction points on the two axes. To locate the center of the image with progressively increasing precision, this procedure is repeated with the next smaller aperture, and so forth down to the smallest aperture. Then a final precise centering operation is performed by searching for the maximum photodetector output or other suitable indication while using the smallest aperture.

Once the center has been located, the encircled-energy measurement begins with the recording of the photodetector response with the smallest aperture in place. Then the responses are recorded with successively wider apertures, using the translation stage and fiducial marks to ensure the concentricity of each successively selected aperture. The photodetector responses thus recorded constitute the desired raw encircled-energy data.

This work was done by Douglas B. Leviton and Sridhar M. Manthripragada ofGoddard Space Flight Center. GSC-13872