1、Best Practices Entry: Best Practice Info:a71 Committee Approval Date: 2000-03-17a71 Center Point of Contact: GSFCa71 Submitted by: Wil HarkinsSubject: Star Image Metrology Part 1: Visual Measurements Practice: The fundamental behavior of a spaceborne (or space-related) optical imaging system is cont
2、ained in its response to an impulse, i.e., a point source. The point source image is referred to by a variety of names: star image, point spread function, far field pattern, impulse response, Fraunhofer diffraction pattern. Here we will use “star image.“ This guideline provides information on instru
3、ments and procedures used in visual star image measurements.Programs that Certify Usage: N/ACenter to Contact for Information: GSFCImplementation Method: This Lesson Learned is based on Reliability Guideline Number GT-TE-2405 from NASA Technical Memorandum 4322A, NASA Reliability Preferred Practices
4、 for Design and Test.Benefit:Star image measurements provide the primary means of appraising the end-to-end health of an optical imaging system. These tests represent good engineering practice, and are reliable indicators of system performance. Star image tests are thus the final arbiter of quality
5、control. A system passing the star tests discussed here ensures that the optical instrument is performing in a reliable manner.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Visual inspection of the star image pattern is a simple and efficient means
6、 of determining whether a problem exists. If something is wrong, important clues as to its nature (e.g., decentered component, inappropriate conic constant) can be provided.Implementation Method:1. Description of Star Image Test ApparatusThe basic equipment needed to perform laboratory star image vi
7、sual measurements is indicated in Figure 1. The optical system on the left half of the drawing is a Star Simulator. This is a Collimator with a back-illuminated pinhole located in the focal plane. The Collimator can be either reflective or refractive, and its pupil should be larger than the imaging
8、system being tested. The pinhole represents the star, and its diameter should be smaller than the Collimator Airy Disc, (i.e., unresolved). Depending on the application, the pinhole back-illumination can be either from a coherent or incoherent source. An example of the former is a laser; the latter,
9、 a point arc lamp. Between the source and the pinhole there is usually some coupling optics to maximize the power through the pinhole, and to fill the aperture of the Collimator with light. (Caution: The pinhole acts like a “pinhole camera.“ If a coiled filament lamp is used, an image of the coil wi
10、ll be formed on the collimator pupil and the output irradiance will be quite nonuniform).refer to D descriptionD Figure 1. Basic layout of a star image test setup A support structure is needed to hold the optical system under test. This mounting fixture should provide modest azimuth and elevation ti
11、lt control to allow alignment of the “test system“ to the Collimator optical axis. The test support fixture should also allow the “test system“ to be accurately rotated through its operational field of view. For refractive “test systems“, the rotation axis should ideally pass through the systems rea
12、r nodal point. A mechanical support fixture that accomplishes this is called a T-Bar Nodal Slide (Reference 1). However, for catadioptric and reflective systems rotation through the rear nodal point is impractical because this point is usually far removed from the physical embodiment of the “test sy
13、stem.“ In this Guideline, the rotation axis will be at, or near the entrance aperture of the “test system.“For visual measurements the “test system“ star image needs to be magnified. This can be Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-accompl
14、ished using a high quality microscope. The microscope objective should be well-corrected for both axial color and spherical aberration. Its numerical aperture must be sufficient to collect all the light from the “test system.“ The eyepiece must also be of good quality, and contain at least a cross-h
15、air reticle to provide reference lines. The reticle plane will be coincident with the image formed by the objective. The microscope should have micrometer controlled XYZ-translation capability.2. Ideal Star ImageThe structure of the star image is controlled by diffraction and aberrations in the imag
16、ing system. If aberrations are negligible, the system is said to be diffraction-limited. For a given focal length, the size and shape of the stop (i.e., the limiting aperture) determines the size and shape of the star image. This is considered the best one can do. The diffraction-limit is a benchmar
17、k or standard by which all other imagery is judged. Since most systems have circular unobscured stops, the resultant star image has a special name. It is called an Airy pattern and is shown in Figure 2.The central core is called the Airy Disc (and is measured across a diameter to the center of the f
18、irst dark ring). Figure 3 (a making the first dark ring as dark as possible; minimizing the power in the first bright ring). This establishes the location of paraxial focus. Offset Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-the microscope latera
19、lly until the center of the cross-hair is in the middle of the first dark ring. Note the position on the lateral micrometer. Traverse to the opposite side and place the cross-hair center in the middle of the first dark ring. Note this position on the micrometer. Subtract these two micrometer reading
20、s to obtain the diameter of the Airy Disc. As a confirmation of F-number, substitute the measured Airy Disc value into Eq.1 and solve for f/#.Center the cross-hair on the Airy Disc. Adjust the focus and locate the first zero axial intensity positions on either side of paraxial focus. Note the Z-micr
21、ometer readings for both positions. Subtract these two Z values. Substitute this difference into Eq.2 and solve for f/#.3.2. Axial ColorIn refractive imaging systems we rely on the curvatures, thicknesses, and refractive indices of the glasses used to form a point image at a certain plane. Unfortuna
22、tely, the index of refraction of glass is wavelength dependent, a phenomenon known as dispersion. This is illustrated in Figure 4. A white light collimated input beam is imaged at various points along the optical axis according to color.refer to D descriptionD Figure 4. Dispersion in simple lens res
23、ults in color dependent axial image points To measure axial color (Reference 1), align the “test system“ to the Collimator. A white light source is needed but the source housing should have a provision for supporting narrow band color filters between the source and the pinhole. Five to ten spectrall
24、y separated filters should Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-refer to D descriptionD Figure 5. Axial Color of Complex Lens be enough to sufficiently sample the visible region. (Note: If there is significant spherical aberration, stop th
25、e lens down to about 3/4 of the aperture). Using the microscope, we measure the axial location of the Airy pattern for each filter. A sample plot is shown in Figure 5 for a 6“ f/1.5 airborne surveillance objective.3.3. Primary AberrationsThe success with which one can visually measure an aberration
26、type in the star image depends on the relative purity of the aberration. On-axis there should only be spherical aberration. Off-axis will be a mixture of spherical, coma, and astigmatism. If spherical is well-corrected, coma will tend to dominate small field angles. As field angle increases, a point
27、 is reached where astigmatism and coma are the same magnitude. Thereafter, astigmatism increases at a faster rate than coma, and dominates the larger field angles.3.3.1. Spherical AberrationSpherical aberration (References 2 and 3) arises when different annular zones of a lens focus at different poi
28、nts along the optical axis as illustrated in Figure 6. The location of the minimum blur circle is where the marginal ray intersects the caustic. (In Figure 6 note the point where the marginal ray crosses the next innermost ray. This point starts the caustic which is the envelope of crossover points
29、of adjacent rays.)Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-refer to D descriptionD Figure 6. Ray fan showing the caustic and minimum blur circle (courtesy Dr. John Loomis) We examine the aberrated star image with the microscope and adjust the
30、focus back and forth until we find the minimum blur circle. Using the lateral translation capability on the microscope, we measure the diameter, Dmb, of this blur circle (in a manner similar to the Airy Disc measurement). Dmbis related to the wavefront aberration coefficient W040(References 1 and 2)
31、 by:(3) Dmb= 4(f/#) W040The above method will generally work for spherical aberration magnitudes above 2 waves. i.e., W040= 2l. Below this a different technique can be used for unobscured systems. (Reference 4). Stop the “test system“ down by centering a small circular aperture in the entrance apert
32、ure. Observe the enlarged diffraction pattern. Move the microscope axially back and forth to identify the best Airy pattern as discussed in Sec.3.1. This establishes the paraxial plane. Note the reading on the micrometer. Remove the small circular aperture. Readjust the microscope axially once again
33、 to identify the best Airy-like pattern. Note the new micrometer reading. Take the difference, d, between the two micrometer readings. This difference can be related to the aberration coefficient by:(4) d = 8 (f/#)2W040By averaging over 10 readings an accuracy of a quarter wave should be Provided by
34、 IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-attainable.3.3.2. AstigmatismAstigmatism (Reference 2 and 3) arises in a system because sagittal and tangential rays from an off-axis point source do not come to a common focus as is illustrated in Figure 7. The i
35、mages formed by the two fans both lie on the chief (or principal) ray but are longitudinally separated. Further, the images formed at these two locations appear as lines orthogonal to each other. These are called the tangential and the sagittal line images.refer to D descriptionD Figure 7. Illustrat
36、ion of astigmatism showing sagittal and tangential ray fans (Modern Optical Engineering) Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Astigmatism can be measured (Reference 1) by determining the separation between the two line foci (along the chie
37、f ray) as a function of field position. (Note: If the “test system“ has a significant amount of spherical aberration it would be helpful to stop the system down to about 3/4 of its aperture). Referring back to Figure 1, we rotate the “test system“ about the rotation axis to some field angle. Because
38、 this rotation does not take place at the rear nodal point, the microscope will have to be translated laterally to reacquire the image. Center the microscope cross-hairs the on the star pattern at medial focus (or circle of least confusion). Adjust the focus of the microscope and locate each line Pr
39、ovided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-focus. Note the Z-micrometer readings. These can be plotted up as a function of field angle, and the separations between the line focii will be readily apparent as illustrated in Figure 8. If higher order
40、 astigmatism is negligible, the longitudinal separation at maximum field angle can be related to the 4th order aberration coefficient by:(5) d = 8 (f/#)2W222refer to D descriptionD Figure 8. Astigmatism plot for Aerojet lens (Ref. 1). Significant higher order astigmatism is present. 3.3.3. ComaComa
41、(Reference 2 and 3) is zonal dependent like spherical aberration. Coma formation is illustrated in Figure 9. (Reference 1). Each circular zone in the lens pupil forms a ring in the image plane. The rings are of different sizes, and are shifted relative to each other as shown in Figure 9 (b). The pat
42、tern resembles an ice cream cone. The chief ray intersects this image plane at the tip of the cone. The line bisecting the coma pattern in the image plane passes through the optical axis. The lines tangent to the ensemble of rings on either side form a 60oangle. The ring from the marginal ray zone i
43、s the largest and its center is farthest from the chief ray intersection point. The paraxial-like zone about the chief Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ray forms the smallest ring and its center is closest to the chief ray. The length
44、from the chief ray to the farthest point on the marginal ring is called tangential coma. The radius of this ring is termed sagittal coma. It can be shown that:(6)Tangential coma = 3 Sagittal coma refer to D descriptionD Figure 9a. Formation of coma from an off-axis object point Provided by IHSNot fo
45、r ResaleNo reproduction or networking permitted without license from IHS-,-,-refer to D descriptionD Figure 9b. Coma pattern Coma is usually measured in the paraxial plane. This means that in addition to moving the microscope laterally to reacquire the image after rotation, some predetermined axial
46、adjustment must also be made to place our point of observation in the paraxial plane. (If a T-Bar nodal Slide is being used, such adjustments are accomplished automatically). Tangential coma is then measured. Tangential coma (TC) can be related to the aberration coefficient at the maximum field posi
47、tion by:(7) TC = 6(f/#)W131Unfortunately, unless coma is pure or heavily dominant, it will be difficult to measure. Unlike axial color and astigmatism, stopping the lens down does not help us because coma, like spherical, is zonal Provided by IHSNot for ResaleNo reproduction or networking permitted
48、without license from IHS-,-,-dependent. Hence, in the presence of competing aberrations, the anchor points for the lateral coma measurement become difficult to define.Note: Further information on star image testing can be found in Reference 6. 4. Indirect Visual Measurements . Knife Edge TestIn this procedure a knife edge (e.g. a razor blade) explores the region around the star image while the observer views the “test system“ pupil directly by eye or on an observation screen. The setup is illustrated in Figure 10. The microscope has bee
