Abstract:
A system for reducing wavelength error caused by angular motion of the moving mirror of an interferometer, such as a Michelson interferometer having fore-optics introducing a beam of radiant energy for impingement on the moving mirror, teaches reducing, without necessary loss of energy, the width of the beam before impingement on the moving mirror; other advantages also accrue to use of the reduced width beam, such as facility in use of absorption cells and multiplying clear path length, when desired.

Description:
FIELD OF THE INVENTION 
     This invention relates generally to interferometry and specifically to foreoptics systems in conjunction with interferometers. 
     BRIEF SUMMARY OF THE INVENTION 
     In brief summary given as cursive description only and not as limitation, the invention teaches reducing wavelength error caused by angular movement of a translating mirror in an interferometer, represented by a Michelson interferometer, by reducing, without necessary loss of energy, the effective width of the beam impinged on the translating mirror. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a plan diagram of an old art interferometer; 
     FIG. 2 is a plan diagram of a second arrangement of old art interferometer; 
     FIG. 3 is a plan diagram of a third arrangement of old art interferomter; 
     FIG. 4 is an optical surface aperture calculation diagram; 
     FIG. 5 is a plan diagram of an exemplary preferred embodiment of this invention; 
     FIG. 6 is a plan diagram of a second exemplary preferred embodiment of this invention; 
     FIG. 7 is a plan schematic showing two angular positions of a moving mirror such as that in a Michelson interferometer and the proportional wavelength error produced by a wide beam relative to a narrow beam; and 
     FIG. 8 is a plan diagram of an embodiment of this invention. 
    
    
     DETAILED DESCRIPTION 
     It is classical to assume that the moving mirror in an interferometer configuration constitutes the aperture of the instrument. When looking at a star or some other such distant source not under our control, the moving and stationary mirrors do constitute the aperture of the system. The concept persists in all aspects of interferometry until this day that the wider the aperture, the better the instrument. 
     A detector in an interferometer system sees only the modulation intensity of the beam that impinges on it. (Thermal effects are another matter, but are not a practical consideration here.) The interferometer then, develops the resulting interferogram, which is intensity-dependent. 
     All instruments of the interferometric type depend on the moving mirror to establish the throughput (intensity) to the detector. An interferometer as an instrument is a modulation device and does not measure the intensity of the beam impinging on it for operation. It is that throughput (intensity) that passes through the interferometer and then impinges on the detector that counts; the detector in an interferometric system sees only the modulation intensity of the beam that impinges on it. In the classical cases mentioned, where the source of the beam is not at our disposal (as in the case of distant stars, for example) it is obvious that the throughput, and therefore the intensity of the beam in question, should be as large as possible. In this way the greatest amount of information possible will be collected and be impinged upon the detector. In fact, in the usual case, the source is used as indicated in the first Figure. 
     FIG. 1 shows old art in the form of a Michelson interferometer I with a source S and collimating mirror C, beam-splitter H, fixed mirror M 1 , moving mirror M 2 , focusing mirror F and detector D. Notice that the amount of light that can be captured on the moving mirror M 2  constitutes essentially the aperture. This arrangement is not very convenient, as for example in working with sample cells. Thus, many, if not all, manufacturers of this type of instrument will bring some modification to it. 
     Current practice usually involves collimating the beam, then narrowing it to a focus in order to pass it through a sample chamber or for any reason whatever, after which it is expanded to original size. Once expanded to original size, it is then collimated again to pass it to the interferometer. This gives the ratio of the initial parallel beam and the reexpanded parallel beam a ratio of 1:1. 
     FIG. 2 shows source S, first collimating mirror C 1 , first focusing mirror F 1 , sample cell A at the focus, second collimating mirror C 2 , and interferometer I, with beamsplitter H, fixed mirror M 1 , moving mirror M 2 , second focusing mirror F 2 , and detector D, in an old art arrangement. 
     Note that again, in FIG. 2, the aperture is essentially that of the moving mirror. 
     FIG. 3 shows an old art arrangement used for convenience in sample cell disposition. Radiation from source S passes to first collimating mirror C 1 , then to the interferometer I in which H is the beamsplitter, M 1  the fixed mirror, M 2  the moving mirror, F 1  a first focusing mirror; A, a sample cell; S 1 , the focus; C 2  a second collimating mirror, F 2  a second focusing mirror, and D the detector. 
     These and many other models of interferometers depend for their throughput on the aperture of the movable mirror. The movable mirror&#39;s aperture is the aperture. Since our invention will relieve the movable mirror of its aperture defining responsibility, a discussion of the aperture of an optical element is necessary. 
     See FIG. 4. Let S be an optical surface. Let f 1  and f 2  be two foci, either one of which may be virtual or real and whose positions in [-∞, +∞] are unspecified. Let the coordinate system be chosen such that the principle ray from f 1  and the x axis coincide. The Effective Clear Aperture of S relative to f 1  is ##EQU1## 
     Where r 1  and r 2  are rays from and to f 1  and f 2  as shown, the tip of r 1  ranging over surface S as the integral ranges over S; 
     1 1  and 1 2  are unit vectors having directions parallel to rays r 1  and r 2  respective; 
     dS is the differential unit of surface S whose direction is normal to the plane of tangency at tip of r 1  and pointing away from f 1 . 
     The expression says that to find the effective clear aperture relative to f 1 , the optical surface is to be divided into infinitesimal elements of area dS and the scalar quantity 1 1 .dS is to be evaluated for each element and the sum taken over the entire surface. If f 1  is at infinity, then the effective clear aperture relative to f 1  and ordinary clear aperture coincide; clear aperture is a special case of effective clear aperture. 
     FIG. 5 shows the invention in embodiment 10, a combination with an interferometer 20 and source S, focusing mirror 22, collimating mirror 24 producing parallel beam B 2  narrower than effective clear aperture B 1  of focusing mirror 22, sample cell A 1  in beam B 2  if desired, the interferometer 20 with beam-splitter 26, fixed mirror 28, movable mirror 30, diagonal mirror 32 if desired, alternate sample cell A 2 , if desired, second focusing mirror 34 and detector D. 
     One advantage to the invention is that optics which are highly efficient in increasing throughput, but had previously been thought useless to this application, can be employed at great benefit. FIG. 5, for example, features an ellipse, depicted as focusing mirror 22. FIG. 5 is by no means the only invention embodiment. 
     FIG. 6 shows the invention, using more conventional optics, in embodiment 40, a combination with an interferometer 50 and source S, first collimating mirror 52, first focusing mirror 54, second collimating mirror 56 producing a parallel beam B 2  narrower than effective clear aperture B 1  (parallel beam) of the first collimating mirror, sample cell A 1  in beam B 2  if desired, the interferometer 50 with beamsplitter 58, fixed mirror 60, moving mirror 62, diagonal mirror 64 if desired, alternate sample cell A 2 , if desired, second focusing mirror 66, and detector D. Also, the design in FIG. 5 and the design in FIG. 6 may act in conjunction to produce a still narrower beam. Other designs will be apparent to one skilled in the art, from the invention. 
     A most important advantage of this invention appears here. The use of the relatively narrower beam of light B 2  loosens the wobble tolerance demands on the moving mirror. When a beam of given flux density (intensity) strikes a moving mirror, it is essential that there should be no angular distortion, or wobble, in the mirror movement. If the mirror does not move exactly parallel to itself, distortion in the interference wavelengths will occur. In fact, the usefulness of the entire interferometer is much impaired if the distortion is much greater than λ/10. As a result, present manufacturers have indeed gone to great lengths to guarantee parallelism in the movement of their mirrors. 
     However, in using a narrow beam of the same flux density (intensity) on the same mirror, the same amount of wobble, or angular displacement in the movement of the mirror, will cause much less distortion to be passed on to the detector. This is because the increase or decrease in distortion (all other factors remaining equal) is mathematically a ratio of the width of the beam. That is, it is ratio of the measurement of the sides of the similar triangles formed. That is λ 1  /λ 2  =B 1  /B 2 . 
     FIG. 7 details the aspect. Two positions M 2 , a and M 2 , b of the moving mirror M 2  diagram a wobble through angle &#34;a&#34;. Because beam B 2  impinges on the mirror in a smaller spot or one having less extent along the mirror, the displacement λ 2  is proportionally less for any given angle &#34;a&#34; than that, λ 1 , for wider beam B 1 . 
     So, given two beams of light of the same flux density, we can say that the narrower the beam the smaller the change in λ as it impinges on the moving mirror and the smaller the amount of distortion. 
     There are several other advantages represented by embodiment 10, illustrated in FIG. 5. There is no loss in throughput. It is immediately obvious that if the same source is used and the same off-axis parabolic mirror is used, the entering rays focused on the detector (assuming that, in the interest of comparison, the sample cells are empty in all cases) are of the same intensity in FIGS. 1, 2, 3 and 6, neglecting losses from first surface mirrors. 
     Thus, novelty of our invention resides in controlling the emitting flux density from any configuration of fore-optics at all in a small envelope and thus being able to use, as a consequence, a smaller mirror. Also, the small envelope can be sent directly, without focusing, through many sample cells, and multiple pass configurations. It has use in double pass systems, too. 
     FIG. 8 shows embodiment 600, similar to that of FIG. 6, except that the fixed mirror 630 may be a unitary array of contiguous dihedral mirrors, 630&#39; and the moving mirror 632 may be a similar unitary array of contiguous dihedral mirrors 632&#39; opposed in complementary relation to the fixed mirror. 
     This Figure demonstrates how a beam B 2  narrow relative to beam B 1  permits us to achieve a very long optical path difference in a small space. If the moving mirrors are caused to move a path difference if 1 cm, then the optical path difference will be twice the number of mirrors less one in the configuration, that is the O.P.D.=2(n-1), where n equals the number of mirrors. It will be apparent to one skilled in the art that the number of mirrors used can be extended at the desire of the instrument designer. Since an extremely narrow beam will allow for miniaturized mirrors, it is apparent that many mirrors can be utilized with ease, producing a very long Optical Path Difference. This is important, since the relationship, resolution=1/O.P.D. cm -1 , expressed in reciprocal centimeters, demonstrates that it is highly desirable to have a long path length in an interferometer. 
     With the advent of replication, the unitary arrays of dihedral mirrors described are easily fabricated. 
     Other schemes incorporating the essential ideas in this Figure can be employed by those skilled in the art. 
     In the examples, the concave mirrors shown may be conventional first surface off-axis parabolas, except where noted as in FIG. 5, where the focusing element is an ellipse. 
     Any reduction in size of input beam will proportionally improve mirror wobble or tilt. Because the intensity of the beam is increased by 1/R 2  as it is narrowed, narrowing the moving mirror impinging beam to a value substantially below 95% of the effective clear aperture of the first collecting optic can bring significant advantages, the narrower the greater the gain, down to a lower limit. 
     A lower limit on gain in narrowing the beam would be imposed by diffraction dependence of the aperture, the first minimum occurring at 1.22 λ/a for a circular aperture; wavelength dependence of the circular aperture is a practical consideration that will be apparent to those skilled in the art. 
     This invention is not to be construed as limited to the particular forms disclosed herein, since these are to be regarded as illustrative rather than restrictive. It is, therefore, to be understood that the invention may be practiced within the scope of the claims otherwise than as specifically described.