An improved procedure for visual microinterferometry in moderately monochromatic light

An improved procedure for visual microinterferometry

in moderately monochromatic light

Ma k s y m il ia n Pl u t a

C en tral O p tical L a b o ra to r y , ul. K am ion k ow sk a 18, 0 3 - 8 0 5 W a rsz a w a , P olan d .

A new p roced u re is prop osed for visu al m icro in te rfe ro m e try in m o d erately m o n o ch ro ­ m a tic lig h t. I t con sists in d eterm in ing o p tica l p a th difference (8) from th e relatio n <3 = c lpv/bpV, w here A ^ is th e v isu al p eak w avelen gth , bpv is th e visual in terfrin g e spacing of an in te rfe re n ce p a tte rn , an d c is th e frin g e d isp lacem en t caused b y th e o b je ct u nd er s tu d y . A ll th ese q u an tities a re sim u ltan eou sly m easu red using a single in terferen ce sy ste m (B io la r P I double re fra c tin g in terferen ce m icro scop e).

1 . Introduction

I t has been found [1] that typical interference (metallic-dielectric) filters of IF - and SIF-type introduce errors into an interference measurement of optical- path difference in long- and short-wave regions of the visible spectrum. These errors result from the fact that interfringe spacings observed in a moderately monochromatic light are different from those in highly monochromatic light (e.g., laser light) of the wavelength X coinciding with the peak wavelength Xp of the light maximally transmitted by the interference filter. This phenome­ non is illustrated in Fig. 1 (taken from [1]) which refers to the biréfringent prism no. 2 of Biolar P I double-refracting interference microscope.

Graph 1 in Figure 1 presents the relationship between highly monochromatic light wavelength and interfringe spacing b of the interference field, measured with the aid of a micrometric phase screw PS (Fig. 2) of the interference micro­ scope mentioned above. Graph 2, in turn, illustrates the same dependence, but when a white-light source (e. g., halogen lamp) is used, and is filtered by means of typical interference filters (IF). As can be seen, interfringe spacings b observed in blue and greenish-blue light, are larger than those resulting from graph 1. The reversal divergence occurs in red light. Both the graphs overlap only within the middle region of the visible spectrum, corresponding to the maximal sensitiv­ ity of human eye. As a consequence, interfringe spacing bmm observed with the filters (IF), and then measured, slightly differs from the real one bhm which occurs in the highly monochromatic light. I t should be pointed out that the values of bhm are in a good agreement with the theoretical data [1].

Deviations of bmm(X) graph from bhm (A) graph are just the source of signif­ icant errors in the measurements of optical-path difference in short- and long­ wave regions of the visible spectrum [2]. In order to avoid these errors it is necessary to employ miltidielectric interference filters (DIF), as was stated in

40 M. Plu ta

P ig . 1. R elatio n betw een th e lig h t w avelen gth (A) and th e in terfrin g e sp acin g (b) fo r th e b iréfrin g en t p rism no. 2 of B io la r P I double re fra c tin g in terferen ce m icro scop e. S tra ig h t line bfim - fo r h igh ly m o n o ch ro m atic lig h t (eq u iv alen t to th e o re tic a l p lo t), cu rv e bmm - for m o d e ra te ly m o n o ch ro m a tic lig h t e x tra c te d from a w h ite lig h t sou rce (halogen lam p ) b y using ty p ic a l in terferen ce filters

H

P ig . 2. D ouble re fra c tin g a tta c h m e n t to B io la r P I in terferen ce m icro scop e. P S - p hase screw (m icro m e tric screw ) fo r m easu rin g in terfrin g e sp acin g b and fringe d isp lacem ents c, H - handle fo r chan gin g b iréfrin g en t p rism s (in p osition i t is show n th e p rism no. 2 is included in to th e p a th of lig h t ra y s)

[1,2], which arc characterized by a more slender spectral profile of transmittance than that for popular metallic-dielectric interference filters (IF and SIF). It occurs, however, that this requirement may be moderated and replaced by a sim­ ple remedical measure, not noticed previously, although it is contained in the theoretical and experimental data given in [1].

2 . Principle of procedure

The measurement of optical path difference is performed in the simplest way- according to a widely-known rule described by the equation

where A - light wavelength, 6 - interfringe spacing, c - interference-fringe dis­ placement due to the presence of the investigated object, e.g., a thin dielectric strip on a glass substrate (Fig. 3). Biolar P I interference microscope [3, 4] has an important advantage, as it allows us to determine in a real-time not only the parameters c and b, but also the wavelength A of light forming the inter- \

b

P ig . 3. Illu stra tio n of E q u a tio n (1)

ference image [1]. The latter measuring possibility results directly from the relation 6(A), represented by graph 1 in Fig. 1. This relation is unique and independent of any instrumental and surrounding conditions. Thus, in order to determine optical path difference <5, the real values of A and 6 need not be sub­ stituted into Eq. (1), but it suffices to substitute the real ratio A/6 which is not charged with errors resulting from the deviation of graph 2 from graph 1 (Fig. 1). For a given light wavelength, the ratio A/6 is a constant (the fundamental feature of the interference system under consideration). This ratio can either be deter­ mined accurately once for good, or determined in a real time; thus avoiding the discussed errors [1] of the measurements in moderately monochromatic light.

The suggested procedure is explained in Fig. 4 which illustrates In an enlarg­ ed scale the upper (a) and lower (b) parts of the graphs from Fig. 1. Let us first consider Fig. 4a. The red interference filter with peak wavelength of Xp being included into the white-light ray path makes Biolar P I interference-microscope

48 M. Plu ta

field of view have interfringe spacing equal to bp. Visually, however, we can discern not the spacing bp, but a smaller one bpv which will be called a visual interfringe spacing. The latter being measured in the visual observation of inter­ ference-fringe field. The measurement is carried out with a phase screw PS (Fig. 2), coupled with a transversal move of biréfringent prisms of Biolar P I

F ig . 4. T op p a r t (a) an d b o tto m p a r t (b) of tb e g rap h s given in F ig . 1, in an en larged scale

microscope. Yet, this measured value of bpv (Fig. 4) should not be attributed to the real peak wavelength (Xp), but to the visual one (Xpv). I t occurs that the ratio Xpvlbpv is practically the same as %p lbp, since, as has been shown in Fig. 1, the graph of bhm is almost an ideal straight line [1]. Similar situation occurs when the red interference filter is replaced by a blue one (Fig. 4b). This time, however, the visual interfringe spacing (b^p) is greater than the real one (bp) and to this end of the spectrum the wavelength l pv slightly greater than l p resulting from the graph bhm(X) should be ascribed. The graph bhm{X) obviously should be prepared using highly monochromatic light. This is a one-time work if done accurately, its result is valid for good (for a given of Biolar P I microscope).

A validity of the suggested procedure is confirmed by the Table which is the extended version of Table 5 taken from [1]. The extended part thereof consists of the columns 5 -9 . As can be seen, the values of the ratios Xpvlbpv in short- and long-wave regions of spectrum are the same as those of the real ratios Xplbp (compare columns 7 and 6). The same cannot be said about the ratios Xp lbpv and Xpvlbp which differ from each other (compare the column 8 and 9) and deviate significantly from the correct values expressed by Xplbp and Xpvlbpv. In the middle region of the visible spectrum all the four ratios are obviously the same. Their divergence, i.e., the deviation of Xplbpvand Xpvlbp ratios from Xplbp and Xpv/bpvm short- and long-wave regions of the visible spectrum will decrease by employing more monochromatic filters of DIF-type instead of the interference filters of IF - and SIF-type (see the last five rows of the Table).

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£ 4 P-4 £ 4 H H h H ■— 1 »— 4 H B t— 1 H H h-4 b-1 b-i ►— 1 H-1 H H t— 1bb H H H H U2 m m m 4 — Optica Applicata XV/1/85 D I P 5 4 6 0 .5 4 9 0 1 8 7 .2 1 8 7 .2 0 .5 4 8 5 2 9 3 .0 2 9 3 .0 2 9 3 .3 2 9 2 .7 D IP 6 3 2 0 .6 3 7 5 2 2 1 .3 2 2 0 .8 0 .6 3 8 5 2 8 8 .7 2 8 8 .5 2 8 8 .1 2 8 9 .2 D IP 6 5 7 0 .6 5 8 5 2 2 8 .4 2 2 8 .6 0 .6 5 8 0 2 8 8 .1 2 8 8 .1 2 8 8 .3 2 8 7 .8 D IP 6 9 5 0 .6 9 7 0 2 4 2 .4 2 4 3 .0 0 .6 9 6 0 2 8 6 .8 2 8 7 .1 2 8 7 .5 ___________ 2 8 6 .4

50 M. Plu ta

According to the results presented above, Eq. (1) can be rewritten as

This equation is practically equivalent to the equation

The latter requires, however, that the wavelength ).p be known and that inter- fringe spacing bp, not observed in the interference image in short- and long-wave regions of spectrum be formally ascribed to it. Moreover, Biolar P I microscope cannot be used for measurement of the wavelength kp of moderately monochro­ matic interference filters, and another instrument, e.g., a spectrophotometer, should be applied. This obviously refers only to moderately monochromatic filters (light sources) from short- and long-wave regions of spectrum and to visual measurement of their wavelength. If, however, a photometric measurement was made by means of a photo-receiver of the identical sensitivity within the whole spectral visible region, then the discussed problem would not exist at all.

3 . Conclusions

Summing up, it should he stated that the procedure given above allows us to use the moderately monochromatic interference filters (IF or SIF) with Biolar P I double-refracting interference microscope. Then the measurement of optical-path difference is practically not charged with errors resulting from the deviations of the graph bmm (A) from the graph bhm (A). I t goes without saying that the wave­ length lpv read from the graph bhm (Fig. 1) must be expressed in the same units as the visual interfringe spacing bpv measured directly with a phase screw FS (Fig. 2), of Biolar P I microscope. I t is convenient to express the parameter c in the same units, also measured directly with the aid of the mentioned phase screw. It is the only parameter being permanently measured, since it suffices to determine the ratio A.pvlbpv in a given experiment only once as soon as a given interference filter is employed. Peak wavelength of the interference filters changes, however, with time, thus the ratio Apvlbpv must he from time to time carefully checked. The plot bhm (A) does not change with time, that is why it should be prepared in an exceptionally careful and exact way, best of all with laser light (He-Ne-, Ar-, Cd-He lasers). In fact, the graph bhm (A) is nothing but a scaling of the interference system. I t should be emphasized that this graph agrees with the theory [1] very well.

The suggested procedure is valid not only when the fringe interferometry, but also the uniform one is applied. Taking advantage of [1], the presented procedure, without a separate discussion, can he easily generalized onto the

uniform interferometry in Biolar P I interference-microscope system. This procedure has a universal character and is applicable in a visual interferometry realized by means of any interference system which has a persistently determin­ ed relationship between the light wavelength and the interfringe spacing.

Rcferences

[1 ] Pl u t a M ., O p tica A p p lica ta 12 (1 9 8 2 ), 1 9 -3 6 .

[2 ] Do b a u K ., Pl u t a M ., P rz e g lą d W łók ien niczy (in P olish ) 3 6 (1 9 8 2 ), 4 9 - 5 2 . [3 ] Pl u t a M ., J . P h y s. E (S ci. In stru m .) 2 (1 9 6 9 ), 6 8 5 -6 9 0 . [4 ] Pl u t a M ., O p tica A c ta 1 8 (1 9 7 1 ), 6 6 1 -6 7 5 . Received August 30, 1984 Усовершенствованная микроинтерферометрическая процедура в умеренно монохроматическом свете Предложены новые действия в визуальной микроинтерферометрии в умеренно монохроматичес­ ком свете. Они заключаются в определении разности оптического пути (<5) по следующей формуле 5 = с13>г/6рг где - визуальная вершинная длина световой волны, Ьрк - отвечающее этой волне межспектральное расстояние интерференционного поля, с - отклонение интерференционных спек­ тров, вызванное исследуемым предметом. Эти все параметры измеряются одновременно с помо­ щью одной интерферометрической системы (интерференционно-поляризационного микроскопа Вю1аг Р1).