Process for the determination of an assembly having isotropic oblique reflection in an extensive spectral region and assemblies obtained by this process

Abstract

A reflecting assembly for polarized white light includes at least one mir associated with a birefringent compensator preventing the reflected light from having a large phase anisotropy. The mirror or mirrors are metallic and covered with a protective silica layer having a geometric thickness of from 0 to about 400A. The birefringent compensator is a crystalline plate of predetermined thickness depending upon the thickness of the protective layer. Known compensators may be used in place of the birefringent plate.

Description

The present invention relates to a process for the determination of a reflecting assembly which does not affect the state of polarization of an oblique incident wave, in an extensive spectral region. It likewise relates to the assemblies having isotropic oblique reflection thus obtained.

The invention applies in particular to all instruments using polarized light when it is necessary to bend the beam for reasons of space. This is particularly the case in modern optical microscopes using polarized light, in which it is an advantage to introduce auxiliary systems such as zoom or a pupillary relay between the objective and the eye-piece, without increasing the height of the instrument as a result. Up to now, it has been impossible to bend the beam without disturbing the state of polarization of the incident wave.

Actually, it is known that any oblique reflection of a polarized wave on a metallic surface is anisotropic. This is due to the inequality of the reflection coefficients corresponding to the states of polarization parallel (polarization:p) and perpendicular (polarization:s) to the plane of incidence. These coefficients generally have a complex expression of the form re.sup.j.sup..phi. and may differ either by their modulus r or by their phase .phi.. The inequality in the moduli leads to a rotation of the direction of incident polarization which can easily be compensated by rotation of the polarizer, while the inequality in the phases leads to transforming a rectilinear incident vibration into an elliptical reflected vibration. When these two inequalities coexist, corresponding to a rectilinear incident vibration there is an elliptical reflected vibration, the major axis of which does not coincide with the direction of the incident polarization.

In practice, this anisotropy of phases is expressed by two impossiblities:

IMPOSSIBILITY OF OBTAINING AN EXTINCTION BETWEEN CROSSED POLARIZERS PLACED ONE AT EACH SIDE OF A MIRROR AND HAVING ANY ORIENTATION;

IMPOSSIBILITY OF MEASURING, BY COMPENSATION, THE BIREFRINGENCE OF AN OBJECT PLACED IN FRONT OF A MIRROR.

Various partial solutions to this problem are known. For example, it is possible to compensate a first mirror by a second, identical to the first, on condition that their planes of incidence are perpendicular. The vibration parallel to the plane of incidence of the first becomes perpendicular to that of the second, and vice versa; this solution, proposed by CAPDECOMME, has the disadvantage of complicating the optical arrangement considerably and is not always compatible with the available space.

It is also possible to dispose, between two mirrors working under the same conditions, a half-wave crystal plate orientated in such a manner that it permutes the vibrations parallel and perpendicular to the plane of incidence. In this case, however, the compensation is only effective for the wavelength for which the plate is half-wave, hence the impossibility of working with complex light and more particularly with white light. In any case, this solution, like previous one, has the disadvantage of having recourse to two mirrors or at least to an even number of mirrors.

Nor does a total-reflecting prism constitute a solution; it does not have any anisotropy of amplitude but the anisotropy of phase is considerable (about 51.degree. for a glass of incidence 1.6) and substantially constant in the visible spectrum.

It is also known to compensate, for a given wavelength, the anisotropy of phase of any mirror or of a total-reflecting prism, by a birefringent compensator; but this compensation is not valid in an extensive spectral region and in particular in white light. This is the case, in particular, with the conventional aluminium mirrors which are protected by a coating of silica having a thickness of the order of 1000 A.

FIG. 1 is a table of the values in degrees of the anisotropy of phase for an aluminum mirror coated with silica having a thickness of about 1000A;

FIG. 2 is a table of values of the coefficients of the index of aluminum and silver;

FIG. 3 is a series of curves showing in full line curves of the differences in phase depending on wave length for an aluminum mirror receiving a beam of polarized white light at an incidence of 45.degree. corresponding to thicknesses of the protective layer from 0 to 1020A and in broken lines curves relating to quartz plates of various thickness;

FIG. 4 is a table of values for a bare aluminum mirror showing anisotropy of phase, the anisotrophy of phase in degrees introduced by a quartz plate and the residue of compensation;

FIG. 5 is a series of curves over the visible spectrum of the value in degrees of the residue of compensation for a bare aluminum mirror;

FIG. 6 is a table of values similar to FIG. 4 for a bare silver mirror;

FIG. 7 is a table of values for an aluminum mirror covered with a protective layer of silica 150A thick;

FIG. 8 is a diagrammatic showing of polarized light reflected from a mirror and passing through a crystalline birefringent plate; and

FIG. 9 is a showing similar to that of FIG. 8 in which the crystalline birefringent plate is replaced by an equivalent compensator.

The table of FIG. 1 gives, in its first line, the values in degrees of the anisotropy of phase introduced by such a mirror for an incidence of 45.degree. and for the whole of the visible spectrum. In order to retain zero anisotropy in the middle of the spectrum, it would be necessary to use a 60-micron-wave quartz plate which produces a birefringence of 360.degree. for this wavelength. The second line of the table indicates, in degrees, the anisotropy of phase introduced by this quartz plate depending on the wavelengths of the spectrum. The third line of the table gives the compensation residue, that is to say the difference in phase existing after reflection of the beam of the mirror and passage through the quartz plate. It will be seen that in fact here the birefringent compensator only provides real compensation in a very narrow zone about the middle of the spectrum; on the contrary, it increases the defect as soon as there is a very slight movement away from this median wavelength. It would be the same if a precise correction were aimed at on another wavelength.

The object of the present invention is to permit the constitution of an assembly associating a birefringent compensator with one or more mirrors, so that this assembly can be used in polarized light in an extensive spectral region. The invention relates to a process for the determination of the characteristics of the elements of this assembly and likewise relates to the assemblies thus constituted.

The invention applies to an assembly consisting of at least one metallic mirror, which may or may not be covered with a thin layer of transparent dielectric, with which there is associated a crystalline compensator device equivalent to a thin plate.

According to the invention, for a given incidence, the thickness of the dielectric layer of the mirror or mirrors and the thickness of the compensating crystal plate are determined depending on one another, working out by calculation:

on the one hand the variation in the difference in the complex coefficient phases of reflection on the mirror or mirrors, relating to the polarization parallel to and to the polarization perpendicular to the plane of incidence, and this for different thickness of the dielectric, depending on the wavelength, in the spectral region under consideration,

on the other hand the variation, depending on the same wavelengths, in the difference in the phases, relating to these two directions of polarization, introduced by the passage through the crystal plate, for different thicknesses of the plate,

finally the variation, depending on the same wavelengths, in the residue of compensation for the differences in phase for each assembly associating in pairs a thickness of crystal plate and a thickness of mirror dielectric, in such a manner that the respective differences in phase are equal in absolute value and of opposite sign for the median wavelength of the spectral region under consideration,

the final selection of the pair of thicknesses being made taking into consideration the minimum thickness of dielectric compatible with the mechanical behaviour of the mirror when this factor is determinant, or taking into consideration the maximum permissible residue of compensation when the use of the mirror allows the corresponding thicknesses of dielectric to be accepted.

The invention will now be described in more detail and will be illustrated by four specific examples of embodiment.

First of all, it may be recalled that for a metallic mirror protected by a layer of dielectric, the reflection coefficient corresponding to a state of polarization p or s is expressed by the formula: ##EQU1## in which: r, (rp or rs) is the modulus of the complex reflection coefficient for the polarization p or s.

.phi. (.phi. p or .phi. s) is the phase of the complex reflection coefficient for the polarization p or s.

r1, (r1p or r1s) is the real reflection coefficient air-layer for the polarization p or s,

r2, (r.sub.2p or r.sub.2s) is the modulus of the complex reflection coefficient metal-layer for the polarization p or s.

.alpha. (.alpha.p or .alpha.s) is the phase of the complex reflection coefficient metal-layer for the polarization p or s.

.beta. = 4 .pi.(d/.lambda.)n1 cos i1

with

.lambda. = wavelength

d = thickness of the layer

On the other hand it is known that ##EQU2## with i0 = angle of incidence

i1 = angle of refraction in the layer

i2 = complex angle of refraction in the metal

These angles being connected by the relationships

n0 sin i0 = n1 sin i1 = n2 sin i2

in which

n0 = (real) index of the air

n1 = (real) index in the layer

n2 = (complex) index in the metal = n - jk

It should be noted that the complex index n - jk in a metal such as aluminium or silver is not an absolutely constant data but may vary very substantially depending on the method of producing the metallic layer. For the examples given below, the coefficients of the index of aluminium and of silver had the values given in the table of FIG. 2.

Knowing the angle of incidence i0 and the optical characteristics of the metal and of the layer, it is therefore possible, for a given thickness of layer and a given wavelength, to obtain the phase .phi.p and the phase .phi.s corresponding to the states of polarization p and s, and to deduce therefrom the difference in phases .phi.p - .phi.s introduced by the reflection on the mirror. It is thus possible to prepare a network of curves giving the differences in phase depending on different wavelengths of the spectral region under consideration, and for various thicknesses of layer.

The graph of FIG. 3 gives, in full lines, such a network of curves relating to an aluminium mirror receiving a beam of polarized white light at an incidence of 45.degree.. The various curves correspond to various thickness of the protective layer of silica, varying from 0 (bare mirror) to 1020 A, this last thickness corresponding to conventional practice for such protected mirrors.

On the other hand, it may be recalled that the anisotropy of phase introduced by a crystal plate is expressed by the formula: ##EQU3## in which: D is the thickness of the crystal plate, is the wavelength of the light,

N.sub.e is the extraordinary index of the crystal,

N.sub.o is the ordinary index of the crystal.

If, in the first instance, the spectral variation in the difference in the indices of the crystal is ignored, it will be seen that the anisotropy of phase varies substantially as the inverse of the wavelength, and for each thickness of crystal, the curve of the anisotropy of phase depending on the wavelength has a hyperbolic shape.

The graph of FIG. 3 gives, in broken lines, a network of curves relating to quartz plates of various thickness.

It will be seen first of all in the graph of FIG. 3 that in order to obtain a compensation for anisotropy of phase which is valid throughout the spectral region under consideration, by the association of a mirror and a crystal plate, it is necessary for the curves of difference in phase relating to the mirror and the plate to be as symmetrical as possible in relation to the axis of the abscissae. If the thickness of the silica deposited on the mirror exceeds 400 A, or more generally if the optical thickness (product of the geometrical thickness by the index) exceeds 600 A, the curve relating to the mirror assumes such a shape that the compensation cannot be effected over the whole of the visible spectrum. This is what was already seen above for a conventional aluminium mirror covered with a layer of 1020 A of silica.

The examples which will now be given will enable the mode of determination of the association of a mirror 10, silica coating 11 and a crystal plate 12 as generally indicated in FIG. 8 with a view to obtaining the improved correction of the anisotropy of phase to be better understood, bearing in mind the mechanical strength requirements of the mirrors.

EXAMPLE 1

A bare aluminium mirror is used, that is to say not covered with dielectric. The table in FIG. 4 gives, in its first line, the values in degrees of the anisotropy of phase introduced by the mirror under an incidence of 45.degree., for the whole of the visible spectrum. The thickness of the quartz plate which brings a precise correction for the median wavelength of the visible spectrum, namely about 5500 A will then be sought. The second line of the table indicates in degrees the anisotropy of phase introduced by this quartz plate 2.17 microns thick, and the third line of the table gives the residue of compensation, that is to say the difference in phase existing after reflection of the beam on the mirror and passage through the quartz plate.

It will be seen that this residue of compensation remains particularly low over the whole extent of the visible spectrum. In fact the maximum defect is only 0.86.degree., in the extreme red, which corresponds to an optical path of .lambda./420.

The residue of compensation varies with the angle of incidence, but it may be noted that it always remains small. The graph of FIG. 5 gives, over the extent of the visible spectrum, the values in degrees of this residue of compensation for this same bare aluminium mirror compensated by a quartz plate of 2.17 microns, and for incidences from 22.degree.30' to 60.degree..

The compensation is all the better, the less the difference between the indices of the crystal varies depending on the wavelength. It is for this reason that magnesium fluoride is even more suitable than quartz, and the last two lines of the table in FIG. 4 give on the one hand the anisotropy of phase introduced by a magnesium fluoride plate 1.68 microns thick, which precisely corrects the bare aluminium mirror for the median wavelength of the spectrum, and on the other hand the residue of compensation. It will be seen that here it is even less than in the case of quartz.

There is no doubt that the use of a bare aluminium mirror is difficult and necessitates special precautions, particularly at the moment when the mirror is mounted in its mount and at the moment when it is cleaned.

EXAMPLE 2

This example is illustrated by the table of FIG. 6 and relates to a bare silver mirror, without dielectric protection. As for the previous example, the thickness D = 3.92 microns of the quartz plate was determined in such a manner as to ensure precise compensation for the median wavelength of the spectrum. The third line of the table gives, in degrees, the residues of compensation. Here it will be seen that aluminium might be preferred to silver for the mirror because the residues of compensation are ultimately greater than in the previous example of a bare aluminium mirror.

EXAMPLE 3

This example is illustrated by the first part of the table of FIG. 7 and relates to an aluminium mirror covered with a protective layer of silica 150 A thick, which corresponds to an optical thickness of 220 A; it gives the residues of compensation here resulting from its associated with a quartz plate 3.39 microns thick. It will be seen that the residues of compensation are higher than in Example 1 but still remain broadly acceptable for numerous application.

EXAMPLE 4

This example is illustrated by the second part of the table of FIG. 7 and gives, under the same conditions as before, the residue of compensation resulting from the association of an aluminium mirror covered with 300 A of silica (optical thickness 440 A) with a quartz plate 4.45 microns thick.

Thus it will be seen that the residues of compensation increase at the same time as the thickness of the protective layer of silica is increased. The final selection will therefore be made depending on the preponderant requirements in the intended application. If an attempt is made to minimize the residual anisotropy of phase in the mirror and compensating plate assembly it would be necessary to accept limitation of the protective dielectric layer to very low values, even to use a bare mirror, which necessitates special conditions for mounting the mirror in the instrument. On the other hand, if it is the mechanical strength of the mirror which is the preponderant element, the minimum thickness of dielectric to be deposited would be fixed first, the thickness of the compensating quartz plate would be determined, and the corresponding residues of compensation could be deduced therefrom.

Everything which has been described previously has been presented in a detailed manner for greater clarity of the explanation. In reality, all these calculations can be effected quickly and easily by a computer.

Needless to say, the invention is not strictly limited to the examples which have been described but likewise covers the equivalent modes of embodiment. Thus, instead of crystal plates, when their thickness is impracticable, recourse may be had to a suitably adjusted compensator, for example of the Babinet Soleil type as generally indicated at 13 in FIG. 9. Similarly, although the examples described relate to the correction of a single mirror, it is likewise possible to compensate a plurality of mirrors by means of a single plate; in this case the thickness of the compensating crystal plate would be multiplied by the number of mirrors, as would the residue of compensation.

Claims

I claim:

1. Optical assembly for the oblique reflection of a beam of polarized light covering a wide spectrum of wave lengths comprising a plane metallic mirror, a protective layer of transparent dielectric on said mirror having an optical thickness of between 0 and 600A, the beam of light impinging on and being reflected by the mirror and protective layer and crystalline birefringent compensating means receiving the reflected light having birefringent compensation equivalent to that of a crystalline plate having a thickness for which the anisotropy of phases created by said means compensates exactly for the anisotrophy of phases created by said mirror for the means wave length of the spectrum of the beam of light.

2. Method of compensating for the anisotrophy of phases created by the reflection of a polarized beam of light covering a wide spectrum of wave lengths by a plane metallic mirror protected by a layer of transparent dielectric having a thickness of 0 to 600A, the steps of directing the reflected beam of light through a birefringent compensating crystalline plate, adjusting the thickness of the plate whereby the anisotrophy of phases created by the plate compensates for the anisotrophy of phases created by the mirror for the mean wave length of the spectrum of the beam of light, determining the adjusted thickness of the plate by measuring the anisotrophy of phases created by the mirror as a function of wave length, preparing a set of curves of the variation of the anisotrophy of phases of the birefringent plate as a function of the wave length and for a series of thicknesses for the plate and then finding the thickness of the plate from the curve providing exact compensation for the mean wave length of the spectrum.

3. Method of compensating for the anisotrophy of phases created by the reflection of a polarized beam of light covering a wide spectrum of wave lengths by a plane metallic mirror protected by a layer of transparent dielectric having a thickness of 0 to 600A, the steps of directing the reflected beam of light through a birefringent compensating crystalline plate, adjusting the thickness of the protective layer as a function of the thickness of the plate whereby the anisotrophy of phases created by the mirror compensates for anisotrophy of phases created by the plate for the mean wave length of the spectrum of the beam light, determining the adjusted thickness of the layer by measuring the variation of the anisotrophy of phases of the plate as a function of wave length, preparing a set of curves of the variation of anisotrophy of phases for the mirror as a function of wave length and for a series of thicknesses of the layer and then finding the thickness of the layer from the curve providing exact compensation for the mean wave length of the spectrum.

4. An optical assembly as described in claim 1 for reflection at an angle of incidence of 45.degree. of white polarized light, the mirror being bare aluminum and the plate being a quartz plate having a thickness of 2.2.mu..

5. An optical assembly as described in claim 4, for the reflection at an angle of incidence of 45.degree. of white polarized light, the mirror being bare aluminum and the birefringent compensating means being a birefringent compensator.

6. An optical assembly as described in claim 1 for the reflection at an angle of incidence of 45.degree. of polarized white light, the mirror being bare aluminum and the plate being a magnesium fluoride plate having a thickness of 1.7.mu..

7. An optical assembly as described in claim 1 for the reflection at an angle of incidence 45.degree. of white polarized light, the mirror being bare aluminum and the birefringent compensating means being a birefringent compensator.