Chungte W. Chen and James B. Breckinridge. A dichromated gelatin off-axis Fresnel zone plate (OFZP) was designed, fabricated, and used in a new type.
Holographic Twyman-Green interferometer Chungte W. Chen and James B. Breckinridge
A dichromated gelatin off-axis Fresnel zone plate (OFZP) was designed, fabricated, and used in a new type of interferometer for optical metrology. This single hologram optical element combines the functions of a
beam splitter, beam diverger, and aberrated null lens. Data presented show the successful application for an interferometric
1.
test of an f/6, 200-mm diam parabolic mirror.
Introduction
Murty' reported the use of two identical Fresnel zone
plates to form a common path interferometer, which is very similar in principle to the scatterplate interferometer invented by Burch.2 Both the zone plates and the scatterplates serve as beam splitters. Smartt 3 described the use of an on-axis Fresnel zone plate to form
a common path interferometer. The advantage of this type of interferometer is that it is less sensitive to vibration and turbulence. However, since all the diffracted orders from the Fresnel zone plate are not completely separated, the fringe contrast and the amount of usable energy contributing to the signal are sacrificed. In addition, it is not easy to fabricate a high-efficiency on-axis Fresnel zone plate that has a uniform spatial frequency response. Hence, the intensity distribution of the interferogram will generally not be uniform. This paper proposes replacing the on-axis Fresnel zone plate with an off-axis dichromated gelatin Fresnel zone plate that has -50% of the diffraction efficiency of the combination of a beam splitter and a diverger. Since it is an off-axis Fresnel zone plate (OFZP) there is no cross talk between the different diffracted orders. Consequently, the noise is less than that of the on-axis Fresnel zone plate case. Also, the 50%diffraction ef-
ficiency of this type of zone plate utilizes energy almost as efficiently as does a Twyman-Green interferometer,
and the fringe visibility is theoretically unity. Since the configuration of this interferometer is similar to that of a Twyman-Green interferometer, it is referred to as a holographic Twyman-Green interferometer (HTGI). In Sec. II the theory of an HTGI is first described. Then, the fabrication of the OFZP, the key element of an HTGI, is discussed, followed by a description of a test
of an f/4, 76-mm (3-in.) diam mirror. The test result is given at the end of the section. To test some mirrors that are not spherical, a conventional interferometer, such as a Twyman-Green interferometer, is normally used in conjunction with a null lens such that the fringes of the interferogram will be straight when the test optics are perfect. Without a null lens the shape of the fringes of the interferogram is generally very complicated, and reduction of the interferogram is difficult. In Sec. III a simple null test using an HTGI is described. To perform a null test for an spheric mirror, the OFZP of an HTGI is replaced by an aberrated OFZP
that functions as a diverger, a beam splitter, and a conventional lens. The result of the null test for an f/6, 200-mm (8-in.) parabolic mirror is shown, and the method of fabricating an aberrated OFZP is discussed. Although many different holographic materials for fabricating an OFZP are available, the high diffraction efficiency and low noise of a dichromated gelatin holo-
gram make it an optimum material.4 The theory of the formation of a dichromated gelatin hologram is given
When this work was done C. W. Chen was with Perkin-Elmer Corporation, Wilton, Connecticut; he is now with Bell & Howell Company, 7100 N. McCormick Road, Chicago, Illinois 60645. James
Breckinridge is with California Institute of Technology, Jet Propulsion Laboratory, Pasadena, California 91103. Received 24 February 1982. 0003-6935/82/142563-06$01.00/0. C 1982 Optical Society of America.
in several references.4 7 The preparation of a dichromated gelatin hologram has been reported by Chang and Leonard 4 and McCauley et al. 5 In Sec. IV a description of tests of the wave front quality of a dichromated gelatin hologram after processing is presented. The low wave front distortion of this hologram makes the technique very promising for fabricating both OFZPs and holographic optical elements suitable for ultralightweight optics. 15 July 1982 / Vol. 21, No. 14 / APPLIED OPTICS
2563
tive beam (0); otherwise the interferogram will show an
I NTERFEROGRAM
array of concentric fringes caused by the defocus and not related to possible wave front errors in the test piece. RM
In principle, the optical configuration shown in Fig. 1(b) is the same as that of Fig. 1(a), except that here the
COLLIMATED0 BEAM
first negative diffracted order of the OFZP is used with the focus behind the OFZP. In Fig. 1(a), the first posTM
(a)
itive diffracted order of the OFZP is used with the focus
in front of OFZP. For a volume hologram, the diffracted intensity is concentrated in a particular dif-
I NTERFEROGRAM
fracted order, for example, the positive first order or the
L
negative first order. To switch the configuration from that shown in Fig. 1(a) to that in Fig. 1(b), the OFZP is
LASER
;U
flipped over such that the incoming collimated beam illuminates the other side of the OFZP.
RM
The configuration used to fabricate an OFZP is shown (b)
Fig. 1.
Holographic Twyman-Green
I '2
\
2
interferometry
L, -,
TM
configuration.
H
in Fig. 2. The beam coming from the Ar-ion laser is divided by beam splitter B. One beam, expanded by lens L1, collimated by lens L2 , and focused by lens L3 , serves as an object beam (0). The other beam is directed by mirror M, expanded by lens L4, and collimated by lens L 5 to serve as a reference beam (R). The angle between beams 0 and R is 30°, and the hologram plane (H) is normal (perpendicular) to the collimated beam. The dichromated gelatin holographic plate is positioned at plane H to record the interference pattern of beams 0 and R. To obtain good quality interferograms for the interferometer, all optics after the pinholes (in Fig. 2) should
Fig. 2.
Setup to fabricate an OFZP.
II. Holographic Twyman-Green Interferometer (HTGI)
The optical configuration of an HTGI is shown in Fig.
1. In Fig. 1(a), the collimated beam from the laser is divided by the off-axis Fresnel zone plate into two beams, U and D. The undiffracted beam (U), which is reflected by the reference mirror (RM), will be split into two beams by the OFZP. The zero-order beam, denoted UU, returns to the laser, and the other beam, denoted UD, will be diffracted by the OFZP. The diffracted beam (D) is reflected by the test mirror (TM)
be of the best quality. The f/No. of the OFZP is determined by the f/No. of the wave front from lens L3. The wave front quality of the object beam (0) and the reference beam (R) is verified prior to the exposing process by the Smartt interferometer and a shear plate, respectively. An f/2 OFZP was made to test an f/4, 76-mm diam aperture mirror; the diameter of the OFZP is -1 cm.
The interferogram of this test mirror is shown in Fig. 3. Both interference beams (UD and DU) have the same intensity, and a high-contrast fringe pattern was obtained as shown. Both the reference beam and test beam pass through the same portion of the OFZP, and
and will also be split into two beams by the OFZP. The
diffracted beam, denoted DD, returns to the laser, and the other beam, denoted DU, passes parallel to beam UD. In this figure, the center of the curvature of mirror TM coincides with the center of the diffracted beam (0). Beam UD, reflected by the reference mirror (RM), serves as the reference beam, whereas beam DU, reflected by the test mirror (TM), is the aberrated test beam. The interferogram (created by the interference of the wave fronts of beams UD and DU) shows the surface error of the test mirror (TM). Lens L relays an image of the test mirror onto the interferogram plane. If the test optic is a refractive element such as a lens, an additional flat mirror is required after the test refractive
element. The front focal point of the test refractive element should coincide with the center of the diffrac2564
APPLIED OPTICS/ Vol. 21, No. 14 / 15 July 1982
Fig. 3.
Interferogram of an f/14, 76-mm diam aperture mirror with
a holographic Twyman-Green interferometer.
BEAMSPLITTFR
An example selected to demonstrate this analysis is an f/6,200-mm diam paraboloid. The surface deviation
MIRROR
from the reference sphere for X = 0.488 gtm is 15X, and
the wave front error is 30X. The conventional interferometry method, as shown in Fig. 5, was used to gen-
PLANE
Fig. 4.
Fig. 5.
Simple configuration to make an OFZP.
Configuration used to make the OFZP for the f/16,200-mm
paraboloid null test.
the wave front distortion introduced into both beams by the substrate of the OFZP is canceled. Consequently, the quality of the substrate of an OFZP is not required to be very good.
Another way to construct an OFZP, as shown in the configuration of Fig. 4, requires only a good collimator
and a good plane beam splitter. Using this configuration, it should be possible to fabricate a low f/No. (i.e., f/1i) and low-cost HTGI.
Since it is known that a di-
chromated gelatin hologram has a uniform frequency
erate an OFZP with -15X fourth-order spherical aberration. The beam from the Ar-ion laser is expanded by L1. Lens L2, an f/3, 25-mm (1-in.) diam doublet with good wave front quality for an infinite conjugate, was utilized to generate approximately -15 waves of spherical aberration by using the wrong conjugate. Lens L3 was used to relay the wave front generated by L2 to the hologram plane, which is perpendicular to the reference beam. A Smartt interferometer was used to verify that the amount of spherical aberration was correct. To have the correct null test, a match should be made, respectively, between the f/No. and surface figure of the paraboloid and the f/No. and amount of spherical aberration of the wave front generated by lenses L2 and L3. Lenses L2 and L3 were moved back and forth until the correct f/No. and the correct amount of spherical aberration were reached. The proper amount of spherical aberration was obtained by adjusting the Smartt interferometer until it was at the paraxial focal plane without any tilt. At that point, the number of fringes was equal to the amount of spherical aberration. Figure 6 is an interferogram of the paraboloid obtained at X = 0.6328 um from a scatterplate
interfer-
ometer without the null test. The many fringes make the interferogram digitization and analysis difficult. In Fig. 7 the interferogram of the null test of this parabo-
response from 100 lines/mm to 5000 lines/mm 3 , uniform
intensity distribution over the whole interferogram is obtained as shown in Fig. 3. Ill. Null Test of a Holographic Twyman-Green Interferometer
A null test of an aspheric wave front using an aberrated OFZP that functions as a diverging lens, beam splitter, and a conventional null lens was performed. The holographic Twyman-Green interferometer configuration shown in Fig. 1(a) was used to analyze the
null test of an aspheric wave front. All wave front amplitudes were assumed to be unity. The phase of the test mirror (TM) can be represented by two components: - W is the phase of a perfect sphere, and Wa is the deviation of the optical surface from this perfect sphere. If the reference mirror is flat, the phase of this mirror willbe 0. Thus, the wave front of the test mirror was written as TM = exp[i(27r/X)(-2W + Wa)], and the
wave front of the reference mirror was written as RM = 1. For the null test the wave front stored in the OFZP
had a phase equal to (W - /2 Wa). When the collimated beam illuminates the OFZP, as shown in Fig. 1(a), the wave front of the undiffracted beam is U = 1, and that of the diffracted beam is D = exp[i(27r/X)(- W
+ /2Wa)]. The interferogram obtained is the interference of beams UD and DU, and the intensity distribution of the interferogram is a constant: I = IUD + UD 2 = 4.
Fig. 6.
Interferogram
of a paraboloid obtained from a scatterplate
interferometer without the null test. 15 July 1982 / Vol. 21, No. 14 / APPLIED OPTICS
2565
MIRROR
COLLIMATED BEAMS HOLOGRAM PLANE
BEAMSPLITTER
Fig. 8.
Fig. 7.
Interferogram
Green interferometer
Setup for a double-exposure holographic test.
of the null test of the holographic Twyman-
for the f6, 200-mm diam aperture paraboloid.
loid, using the holographic Twyman-Green interferometer described above, is shown. A fraction of a wave
of the wave front error shown in the interferogram may come from two sources. These sources are the indirect
method of determining the aberration of the object beam (Fig. 5) and the lack of an independent adjustment for f/No. and wave front aberration. The clear aperture of the Smartt interferometer made by Ealing Co. is insufficient to transmit all the light for large aberration wave fronts. To compute the amount of large spherical aberration obtained with the Smartt interferometer, it is necessary to reduce the size of the clear aperture and check the amount of the corresponding spherical aberration. For example, if 15 waves of spherical aberration for full aperture are desired, the aperture can be reduced to 0.837 times the desired aperture and adjustment made to produce 7.5 waves of spherical aberration. After the correct amount of spherical aberration is obtained, the aperture can be opened to full size. During this type of conversion, the measurement error will contribute to the error of final null test. For example, a 3% beam diam error, which is
