Multiple frequency laser interference microscope

A multiple frequency laser interference microscope in which a source of coherent laser light containing at least two frequencies of light is used in conjunction with a transmitted light polarizing microscope so as to provide an interference microscope. Using a wide fringe mode of operation refractive index becomes directly visible as shades and hues of different colors, and discontinuities and gradients of less than 0.001 may be detected. Using a narrow fringe mode of operation, measurement of fringe shift and thickness permit exact and rapid calculation of refractive index to 0.00n at least.

FIELD OF INVENTION 
This invention relates to interferometers and more particularly to multiple 
frequency laser interference microscopy. 
DISCUSSION OF PRIOR ART 
The phenomenon of interference has, of course, long been recognized as one 
of the most effective means for determining refractive indices, phase 
differences, light source wave lengths and the like and for making 
distance measurements. Numerous interferometers have been described in the 
literature, including signal frequency laser interferometers (vide, for 
example, Canadian Patent No. 833,877 issued Feb. 10, 1970 to Erickson) 
which have been developed to take advantage of the unprecedented spectral 
purity and coherence of laser light. It has now been found that 
significant improvements over single frequency laser interferometers can 
be achieved in the access of refractive index measurement dispersion of 
refractive index, and refractive index gradients among others, using a 
multiple frequency laser interferometer. Using the techniques of the 
present invention accuracies of an order of magnitude greater than 
heretofore possible may be achieved. 
It is axiomatic in interference studies that light of one frequency cannot 
produce interference effects with light of another frequency. It follows 
therefore, that, with mixed light, each frequency of light behaves as 
though the other were not there. Thus, if pure red, green and blue light 
frequencies are mixed and caused to interfere, it would be logical to 
expect the resulting interferogram to consist only of these colours in 
various intensities. As will be demonstrated in more detail hereinafter, 
this has been found not to be the case. In the case of red and green 
light, for example, vivid shades of yellow and other colours are observed 
in the interferogram, but are not, of course, present in the spectrum 
which still only has red and green. The explanation of this somewhat 
unexpected result lies in the difference between frequency and wavelength 
on the one hand, and colour, on the other. Colour is that which is 
perceived by the human eye - frequency is that which is actually present 
in the spectrum. Colour vision in the eye and colour in photographic film 
is the result of combinations of the three primary colours, red, green and 
blue. For example, the eye has no way of determining yellow light directly 
but relies on two receptors which are sensitive to red and green. Thus, in 
the interferogram, red and green light together are perceived as yellow. 
This colour effect has been found to be very useful for detecting and 
dramatically emphasizing slight variations in optical path in many 
practical situations ranging from biological studies of cell tissues to 
geological studies of mineralogical and petrological specimens. 
OBJECT OF INVENTION 
It is, therefore, an object of the present invention to provide a 
multi-frequency laser interferometer useful in determining refractive 
indices and the like. 
Another object of the invention is to provide an improved method of optical 
interferometric determinations using a multi-frequency laser beam as the 
light course. 
BRIEF SUMMARY OF INVENTION 
Thus by one aspect of this invention there is provided an interferometer 
comprising: 
(a) a first laser light source to provide a polarized coherent light beam 
of a first selected frequency; 
(b) a second laser light source to provide a coherent light beam of a 
second selected frequency differing from said first selected frequency and 
parallel polarized relative to said beam from said first laser light 
source; 
(c) means to combine beams from said first and second sources into a single 
beam of mixed said frequencies; 
(d) first optical means to divide said single beam into a reference beam 
and a sample beam; 
(e) second optical means to recombine said reference beam and said sample 
beam so as to cause interference therebetween and produce an 
interferogram; 
(f) a first optical path between said first and second optical means for 
passage therealong of said reference beam; 
(g) a second optical path, between said first and second optical means for 
passage therealong of said sample beam; 
(h) means to interpose a sample at a selected position in said second 
optical path; and 
(i) means to scan said interferogram. 
By another aspect of this invention there is provided in a method for 
making optical determinations by laser interferometry the improvement 
comprising: 
providing a beam of coherent laser light containing at least two parallel 
polarized selected frequencies, splitting said beam into a sample beam 
which passes through a stationary sample under detemrination and a 
reference beam which bypasses said sample, causing said sample beam and 
said reference beam to interfere so as to produce an interferogram 
containing more colours than there are frequencies in said beam.

DETAILED DESCRIPTION 
In order to determine refractive index by interferometry, the difference in 
the optical path between a known and an unknown material is determined and 
compared to a reference beam of fixed, but adjustable optical path. 
Optical path (OP) is defined as the product of refractive index (N) and 
the thickness (t) thus: 
EQU OP=Nt 
If the number of wavelengths in the optical path is M, then 
EQU OP=MLo 
where Lo is the wavelength in vacuo of the light used. For two different 
optical paths due to different refractive indicies: 
EQU OP.sub.1 -OP.sub.2 =(M.sub.1 -M.sub.2)Lo 
The difference in the number of wavelengths is referred to as the shift, S 
(S=M.sub.1 -M.sub.2) and is the fundamental observation. 
The known material acts as an internal standard to permit an absolute 
measurement of refactive index. The interference effect which is measured 
is, of course, due to the difference in optical path between the sample 
and reference beams. These measurements may be made using either a 
"narrow" or "wide" fringe technique. 
In the "narrow fringe" method, the interference fringes are adjusted to be 
significantly smaller than the object being observed, as in FIGS. 2, 3 and 
4. The order of interference for each fringe at any point is determined by 
the optical path difference between the sample beam and the reference 
beam. The interferogram in such a case appears to be a series of coloured 
and dark stripes which are offset at discontinuities and curved at smooth 
gradients of RI. From the above equations, if N.sub.1 is the RI of a known 
material in contact with an unknown of RI=N.sub.2, then in general the 
fringes in an interferogram will be shifted at the boundary according to 
the relationship: 
EQU N.sub.1 -N.sub.2 =S Lo/t 
where S is the observed shift in apparent wavelength in the interference 
pattern, Lo is the wavelength in vacuo of the light used, and t is the 
thickness (in the same units as the wavelength, of course). This is the 
fundamental equation governing interferometric observations. If more than 
one colour of light is present then each colour behaves as if the others 
are not present. The resulting interference pattern is the sum of the 
individual patterns for each energy of light present. 
In particular, note that an accurate RI determination is tied to an 
accurate thickness measurement as well as the shift determination. In 
principle, thickness measurements can be determined quite accurately in 
cases where both refractive indices are known. It is useful to note that, 
because of the form of the equation, if (N.sub.1 -N.sub.2) is small, then 
a rather large error in the thickness may be tolerated with acceptable 
accuracy in the RI determination. This is important because it is 
difficult to measure the thickness of a microscopic particle with better 
than 1 or 2% accuracy. Even this error is entirely consistent with an 
overall error in RI of 0.00n. Table II represents data for an actual 
calculation of the RI of a known sample of optical glass, using a grain 
mount in thermoplastic, the "quick method" of preparing material for 
analysis. 
TABLE I 
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LASER LINES 
COLOUR WAVELENGTH POWER LASER 
______________________________________ 
Red 632.82 nm (2 mw) Helium-Neon 
Green 514.532 nm (9 mw) Argon-Ion 
Blue-Green 
487.986 nm (15 mw) Argon-Ion 
Blue-I 476.486 nm (2 mw) Argon-Ion 
Blue-II 457.935 nm (1 mw) Argon-Ion 
______________________________________ 
Reference: Handbook of Tables for Applied Engineering Science, 2nd 
Edition, 1976, Boltz, R. E., and Tuve, G. L., editors. CRC Press, 
Cleveland, Ohio. Tables 268 and 269. 
TABLE II 
______________________________________ 
SAMPLE CALCULATION RAPID GRAIN 
Standard Optical MOUNT METHOD 
Medium Glass .DELTA. N 
N (calc) Error 
______________________________________ 
A 1.65574 1.55740 0.09834 
1.55828 0.00088 
B 1.67591 1.56800 0.10791 
1.56568 0.00231 
______________________________________ 
For a single determination of a grain of 48.7 micron thickness and shift 
as indicated. Cargile optical glass standard in thermoplastic. 
A = Red light, 632.8 nm He--Ne Laser shift, S = 7.5 fringes 
B = Bluegreen light, 488.0 ArgonIon Laser, S = 11.0 fringes 
In the "wide fringe" method the optics are aligned as precisely as 
possible, so that the centre of "zeroth" fringe becomes very wide 
(ideally, filling the entire field of view). All other things being equal, 
the only differences in the optical path will be due to variations of RI 
within the sample itself. The resulting interferogram now has the 
appearance of a "normal" image. It is a "picture" of the objects in the 
field of view colour-contoured with respect to optical path (FIGS. 5 (a) 
and (b) and FIG. 6). The interferogram may, therefore, be treated as 
though it were a topographic map in which refractive index differences are 
contoured (optical "height" instead of geographic height). Since 
refractive index is directly visible, all optical discontinuities and 
gradients become visible often with startling visual effects. It is 
possible to estimate the actual refractive index gradients by observing 
the interference colour, although the fraction of a fringe shift is, in 
general, difficult to determine. The use of more than one colour of light 
makes it relatively easy to distinguish positive from negative gradients 
in refractive index. 
This is not possible with a single laser frequency and is one of the 
principal advantages of the use of multiple laser frequencies according to 
the present invention. 
It will be appreciated that any feature which affects the refractive index 
becomes visible. Thus chemical composition, structural or crystallographic 
state may become directly visible. Such effects may be seen whether due to 
intrinsic properties of the specimen (chemistry) or its history of 
treatment (i.e. stress effects). If the relationship between refractive 
index and chemical composition in naturally occurring mineral solid 
solutions is considered, for example, the variation in chemical 
composition necessary to yield an observable optical effect may be 
determined. Table III below illustrates some minimal compositional 
variations which can be readily detected by the wide fringe method. In 
some cases, such as garnets (isotropic) and nepheline (uniaxial) only a 
method such as interferometry is capable of rendering optical zonation 
visible. 
TABLE III 
______________________________________ 
MINIMUM VISIBLE ZONING IN MINERALS 
WIDE FRINGE TECHNIQUE 
MINERAL SERIES MOLE % FOR 0.001 N 
______________________________________ 
Olivine 0.5% 
Garnet series 0.5% to 1% 
Enstatite-hypersthene 
0.8% 
Hornblende 1% 
Scapolite (Meionite) 
1.1% 
Aegirine-Augite 1.4% 
Actinolite-Termolite 
1.5% 
Plagioclase 2% 
Nepheline-kaliophilite 
3% 
Sanidine 10% 
______________________________________ 
Note: 
The above Table gives the approximate chemical composition corresponding 
to 0.001 gradient in refractive index for the mineral series indicated. 
Data from various sources. 
An apparatus specifically adapted to carry out either of the above 
discussed methods is illustrated schematically in FIG. 1. Light beams from 
two lasers 1, 2 are combined in a beam splitter 3 to produce a single beam 
of mixed frequency mixed coherent light. Laser 1 is a Helium-Neon 2 m watt 
laser which only lases in the red producing the well known 632.8 nm line, 
and laser 2 is a tunable Argon-Ion 20m watt laser which produces several 
lines in the visible green and blue region as illustrated in Table 1 
above. The single mixed frequency beam then passes through a beam expander 
4. Within this beam of light each frequency is coherent but the different 
frequenices are not mutually coherent. The power output of laser 2 is 
controlled by its power source and this is a convenient method of 
balancing the output of the two lasers to produce a mixed light which, in 
an interferogram, actually contains more colours than there are 
frequencies of light. Additional balance and intensity control is provided 
by blue/green balance filter 5 and variable density filters 6,7. The light 
from both lasers 1,2 is polarized and the lasers must therefore be 
oriented so that the polarization directions are coincident when the mixed 
beam leaves the source beam splitter 3. 
The beam of mixed light then enters the second part of the apparatus namely 
a modified Mach-Zehnder interferometer attached to a polarizing 
microscope. A beam splitter 8 separates the light into a reference beam 9 
which bypasses the the sample 10 entirely via a first surface mirror 11, 
and a sample beam 12 which passes through the sample and contains phase 
information of interest. The reference beam 9 may be "tuned", that is, 
slightly changed in its optical path, by means of a tilting compensator 
13, sometimes referred to as an optical tuner, and further adjusted by one 
or more filters 14. Various filters and compensators, such as a wedge 
compensator 15, may be provided in the path of beam 12 for adjustment of 
the interference pattern. A beam splitter 16 is also desirable so that the 
sample 10 may be viewed either by way of laser beam 12 or by normal white 
light from a white light source 17. A beam dump 18 may also be provided. 
The phase information contained in sample beam 12 is only visible as 
interference fringes where the reference beam 9 interferes with the sample 
beam 12 when combined in beam splitter 19 to produce the interferogram 
which may be scanned or observed and/or photographed through microscope 
20, in conventional manner. The interferogram is composed of fringes of 
equal interference order (optical path difference, in this case) and is 
not, therefore, an image in the strict sense of the term. In the wide 
fringe mode of operation, however, the interferogram is virtually 
indistinguishable from an image but for correct interpretation requires 
the knowledge that it is, in fact, an interferogram. 
With the narrow fringe technique, as described hereinabove, diagnostic 
studies of single particles (see FIGS. 2 (a), 2 (b) 2 (c), 3 (a) and 3 
(b)), fibers and biological materials (FIG. 4), are readily possible. 
Using grain mounts, refractive index may be determined to 0.00 n on a 
routine basis for particles as small as 20 microns. It should be noted 
that only a single particle is needed for this determination. Using the 
wide fringe technique, as hereinbefore described, striking visual results 
are achieved with both geological and biological specimens. FIGS. 5 (a) 
and 5 (b) illustrate a plagioclase phenocryst from Mt. St. Helens, 
Washington (probably not from the eruption of May 18, 1980) and attention 
is particularly drawn to the wealth of fine detail visible. The finest 
zones in the plagioclase are only 5 microns wide, each colour of zone 
represents a different refractive index and hence a different composition 
of plagioclase. The history of growth of the plagioclase is recorded in 
these Figures. The onion cells in FIG. 6 are only about 0.5 mm long and 
the cell nuclei and other features are clearly visible. Note that the same 
cells viewed by the narrow fringe technique (FIG. 4) do not show the 
nuclei nearly as clearly. Because the eye (and photographic film) is 
extremely sensitive to slight changes in colour, refractive index 
gradients corresponding to an optical path difference of at least 1/20 of 
a wavelength are readily visible. This corresponds to a refractive index 
gradient of 0.001 for a 30 micron thick sample or 0.0001 for a 3 micron 
thick sample. 
The use of lasers as the light source in the arrangement of the present 
invention is considered an essential feature of the invention not only for 
their narrow emission lines but also because of their coherence which 
makes interference possible over large distances. Because of this, the 
actual optical paths and the magnitude of the optical path differences are 
not critical and this, in turn, relaxes design criteria for the optics of 
the interferometer, and enables the use of relatively inexpensive standard 
components.