Very Accurate Measurements of Fringe Shifts in an Optical InterferometerStudy of Gas FlowErnst H. Winkler Citation: Review of Scientific Instruments 24, 1067 (1953); doi: 10.1063/1.1770598 View online: http://dx.doi.org/10.1063/1.1770598 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/24/11?ver=pdfcov Published by the AIP Publishing Articles you may be interested in SU-E-T-410: Fringe Stability and Phase Shift Measurements in a Michelson Interferometer for OpticalCalorimetry Med. Phys. 41, 320 (2014); 10.1118/1.4888743 Accurate force measurement using optical interferometer AIP Conf. Proc. 1454, 15 (2012); 10.1063/1.4730677 An optical interferometer for gas bubble measurements Rev. Sci. Instrum. 67, 3564 (1996); 10.1063/1.1147247 Fringe Spacing Changes in Accurate Measurements of Interferometer Fringe Shifts Rev. Sci. Instrum. 25, 923 (1954); 10.1063/1.1771214 Very Accurate Measurement of Fringe Shifts in an Optical Interferometer Study of Gas Flow Rev. Sci. Instrum. 24, 121 (1953); 10.1063/1.1770637

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LABORATORY AND SHOP NOTES 1067

FIG. 3. Secondary container for Cary cells. A. Aluminum box. B. Quartz windows. C. Brass closure. D. Aluminum cover. E. Brass screws.

0.05 density unit. The sensitivity of the Beckman with the photo­multiplier attachment is such that it is possible to use these cells with high resolution over the entire range of the instrument.

Although the various cells described here are vapor tight, nevertheless the possibility of an occasional leak must be vigilantly guarded against, since hydrogen fluoride can be most destructive to optical parts. The Beckman is usually provided with spacers which are inserted between the cell compartment and the optical portions of the instrument. The windows in the spacing plates are simply cut-out sections. To isolate the cells from the rest of the instrument, quartz plates are recessed into these openings, and in event of a leak only the quartz plates need be replaced.

For the Cary instrument, the cells are enclosed in a metal box (Fig. 3) with replaceable quartz windows. It must be emphasized that these secondary containers are an essential part of the equip­ment necessary for studying spectra in reactive fluoride solutions.

The authors gratefully acknowledge the advice and help of Dr. J. C. Hindman in the use of the Cary, J. R. Pickhardt for con­struction of the cells, and J. D. Newcom and E. R. Nowicki of the Argonne Optical Shop for polishing the Fluorothene windows.

1 C. E. Schildknecht. Vinyl and Related Polymers (John Wiley and Sons Inc .• New York. 1952). p. 475-483 .

• J. S. Kirby-Smith and E. A. Jones. J. Opt. Soc. Am. 39. 780 (1949). • J. Schnizlein and R. C. Vogel. Argonne Chern. Eng. Div. (private

communication) .

Very Accurate Measurements of Fringe Shifts in an Optical Interferometer Study of Gas Flow

ER.NST H. WINKLER.

U. S. Naval Ordnance Laboratory. White Oak. Silver Spring. Maryland (Received June 19. 1953)

I N a paper having the above title, F. D. Werner and B. M. Leadon1 have proposed a new method for very accurate meas­

urement of fringe displacements photographed using the Mach­Zehnder or the Michelson Interferometer. The accuracy is claimed to be 1/500 of the fringe spacing. The method is restricted to cases where the loci of points of equal fringe shift are a family of known curves. A brief outline of this procedure is as follows. A photographic negative is made, on a glass plate, of the undis­placed fringe system together with a suitable set of fiducial lines. A second negative is then taken of the displaced fringe system. One of the negatives is copied into a popitive. The negative and the positive are then placed in contact on their emulsion sides and the fringe system lined up with the fiducial lines.

By moving one plate with respect to the other in a direction perpendicular to the fringes, light transmitted through the plates varies depending on the relative position of the two plates. Werner and Leadon suggest utilizing the variation of the transmitted light to make very accurate determinations of displacements in terms of fringe spacing. In case the family of curves of equal fringe displacement are straight lines, the measurements are carried out by illuminating the plates through a narrow slit perpendicular to the fringes and long enough to cover several of them. The transmitted light is observed by means of a photo cell and galva­nometer. The contrast of the two plates may be increased by several high contrast copying processes. The proposed method gives the correct fringe spacing and fringe displacements under the ideal condition that equally spaced fringes do not change their spacing in the displaced position. Actually, slight variations of fringe spacings are present in any interferogram covering an ex­tended field.

We investigate now to what extent the proposed method is affected by a variation of the fringe spacing. We assume that fringe system I can be represented by a photographic density distribution of the form2

fW=i+cos~.

The second system is brought in coincidence with the first system at ~=O and may be expressed in the same coordinate system by

g(~) = 1 +cos[W +0)],

assuming a fractional change 0 in fringe spacing. It is further assumed that system I will be moved by w with respect to system II. Then

fW=i+cos(Hw).

The light intensity transmitted can then be expressed by

J = k Jol f(~)g(~)d~, where k is a constant proportional to the slit width and the light intensity falling on the slit. The length of the slit is represented by I. The distance from 1=0 to the first maximum and the fringe spacing can then be found by dJ /dw=O. Assuming the slit length I is a multiple of the fringe spacing of system I, 1=21fn; n=1, 2,3 .,. and no<1. The resulting expression reduces to

tanw = (1 +0)-1 tanm, or with 0«1 and the extrema corresponding to the fringe spacing are given by

W=lfnO+21fm m=O, 1,2 . ".

The fringe system I has to be moved lfno for the first maxima and thereafter by a multiple of its fringe spacing. With no change in fringe spacing w would be equal to zero, hence would give the correct fringe displacement. With a change in fringe spacing w=!nO if w is measured in the units of the fringe width of system I.

From this result the following can be concluded: (a) Using the proposed method necessitates proving by measurement, with an accuracy surpassing the claimed accuracy of the method, the fringe spacing has not changed; and (b) increasing the number of fringes within the slit does not increase the accuracy of the measurement of fringe shifts if the fringe spacing has changed. For example for a claimed accuracy of 1/500 of the fringe spacing and utilizing five fringes within the slit, the fringe spacing must remain unchanged to 1/1000. From this it is evident that the measurement of fringe displacements cannot be made more precise by employing a number of fringes whose spacings cannot be made known in a sufficiently accurate manner.

Furthermore, one notices that the measurement of the fringe spacing is independent of the number of fringes within the slit, but dependent upon which of the fringe systems is being moved. Moving of system I produces 2 ... , but moving of system II gives 211'(1-15). From Fig. 2 of the Werner and Leadon paper one can see that the two plates have to be moved different distances to

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1068 LABORATORY AND SHOP NOTES

obtain the same alignment. In turn, the fact that the measured fringe spacing, for uniformly spaced fringes, was independent of which plate was moved shows that their spacings were identical.

The author is weH aware of the fact that changes of fringe spacings, such as arise in different fringe locations or are caused by disturbances to be measured, are not uniform as so far assumed for the sake of simplicity but are irregular. If the variations in fringe spacing accidentaHy compensate their effects, the error in measurement then may become smaHer or can even become zero. It should be emphasized, however, that we cannot determine the amount of compensation without measuring the individual fringe spacings with an accuracy which must be greater than that obtainable from the proposed measuring technique.

The experimental test by Werner and Lead on proves that, by moving one of the plates, the location of extrema of the trans­mitted light can be determined with an accuracy of 1/500 of the distance between these extrema, but it fails to establish the fact that the information on the fringe displacement is of the same accuracy.

1 F. D. Werner and B. M. Leadon, Rev. Sci. Instr. 24, 121 (1953) . • A sinusoidal density distribution has been selected for reason of sim·

plicity. Any other distribution which resembles a fringe system produces similar results.

Low Input Capacity Probe G. L. SHULTZ

International Business Machine Corporation, Poughkeepsie, New York (Received June 5, 1953)

A PROBE presenting small input capacity is desirable in many waveform investigations. In general, oscilloscope probes

have an input capacity of 10 micromicrofarads or greater at a 10: 1 attenuation. The probe discussed here presents an input capacity of 4.5 micromicrofarads at a 1.66: 1 attenuation.

The probe circuit as shown in Fig. 1, consists of two cathode-

+150 V.D.C .

• \rV--+---OUTPUT

IMEG.

2000 1.01 U.F. ",100

TO INNER SH[ELD

IMEG.

FIG. 1. Probe circuit diagram.

foHower stages. The first stage was designed with emphasis on low­input capacity. In order to maintain an over-aH pulse rise time of 0.1 microsecond, the second cathode foHower was designed primarily as an impedance matching unit to drive a coaxial line and oscilloscope.

To further reduce input capacity, a double shield arrangement as outlined in Fig. 2, was used. By connecting the inner shield

POLYSTYRENE S PARA ~I

1..----6f'---J SCALE-FULL SIZE

FIG. 2. Outline of probe.

~

% POSITtVE IOUS PULSES

10 [ ./

V 8

• ~R GREATER [NPOTS

• ./ GAID CURRENT IS DRAWN

/ /

I 12 10 a

6 V 2 • 6 • [0 12 I. [6 IB 20 INPuT

2

.,,/ · f-----6

NEGATIVE IOUS. PULSES

FIG. 3. Linearity characteristic.

through a capacitor to the cathode of the first stage, the effect of the capacity between the pickup and inner shield was reduced.

A Sylvania type 6111 subminiature tube was employed. The filament and B+ leads were bypassed to ground to eliminate pickup.

The probe has a high-frequency response which yields a rise time of 0.08 microsecond. A 2.5 kc/sec square wave amplitude is down 5 percent at 115 microseconds duration. Figure 3 indicates that the probe has a linear attenuation of 1.66: 1 for 10 micro­second positive pulses up to 11 volts amplitude and 10 micro­second negative pulses of 6 volts amplitude. With the inner shield grounded, the input capacity is 6.2 micro· micro farads. By using the double shield, the input impedance is 4.5 micro-micro farads and 5.2 megohm. These input capacities were measured on a Q-meter at a frequency of 1.6 Mc/sec.

The writer wishes to express his thanks to J. C. Logue and R. B. DeLano, Jr. for their helpful suggestions.

Electronic Shutter Photographs of Exploding Bridge Wires

w. A. ALLEN, C. H. HENDRICKS, E. B. MAYFIELD, AND F. N. MILLER

Michelson Laboratory, U. S. Naval Ordnance Test Station, Inyokern, China Lake, California

(Received April 27, 1953)

T HE experiment reported in this note is intended to yield some idea of the macroscopic and microscopic phenomena

associated with an exploding bridge wire during the first few j.l.sec of the event. Work with electrically exploded bridge wires is not new. l Previous investigators have studied the spectra,2 tempera­ture,3 polarization,. and brightness6 ,6 associated with this experi­ment. Still photographs7 have been obtained at early stages of the event by means of the magneto-optic effect. The photographs presented in this note differ from those previously published as a result of improved definition made possible by a new instrument. The apparatus used was a magneto-optic device manufactured by Edgerton, Germeshausen & Grier, Inc. The principle of this instrument, known as a Rapatronic Shutter, Type 2208--0, has been described elsewhere.s The effective exposure time of this shutter is less than one I'sec. The bridge wire material consisted of No. 20 B & S aluminum wire, stretched between high-voltage terminals 20 cm apart. The energy, 900j, was applied with a rise time of about one j.l.sec from two 6 kv 25 I'f condensers in parallel.

Figure 1 illustrates the results of the experiment. The top photograph represents the bridge wire stretched between the two high-voltage terminals. The following seven pictures in Fig 1. rep­resent typical stages of the exploding wire at time intervals that

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