ASTM C1648-12(2023)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: C1648 − 12 (Reapproved 2023)
Standard Guide for
Choosing a Method for Determining the Index of Refraction
and Dispersion of Glass
This standard is issued under the fixed designation C1648; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 1.2 This standard does not purport to address all of the
safety concerns, if any, associated with its use. It is the
1.1 This guide identifies and describes seven test methods
responsibility of the user of this standard to establish appro-
for measuring the index of refraction of glass, with comments
priate safety, health, and environmental practices and deter-
relevant to their uses such that an appropriate choice of method
mine the applicability of regulatory limitations prior to use.
can be made. Four additional methods are mentioned by name,
1.3 Warning—Refractive index liquids are used in several
and brief descriptive information is given in Annex A1. The
of the following test methods. Cleaning with organic liquid
choice of a test method will depend upon the accuracy
solvents also is specified. Degrees of hazard associated with
required, the nature of the test specimen that can be provided,
the use of these materials vary with the chemical nature,
the instrumentation available, and (perhaps) the time required
volatility, and quantity used. See manufacturer’s literature and
for, or the cost of, the analysis. Refractive index is a function
general information on hazardous chemicals.
of the wavelength of light; therefore, its measurement is made
1.4 This international standard was developed in accor-
with narrow-bandwidth light. Dispersion is the physical phe-
dance with internationally recognized principles on standard-
nomenon of the variation of refractive index with wavelength.
ization established in the Decision on Principles for the
The nature of the test-specimen refers to its size, form, and
Development of International Standards, Guides and Recom-
quality of finish, as described in each of the methods herein.
mendations issued by the World Trade Organization Technical
The test methods described are mostly for the visible range of
Barriers to Trade (TBT) Committee.
wavelengths (approximately 400 μm to 780 μm); however,
some methods can be extended to the ultraviolet and near
2. Referenced Documents
infrared, using radiation detectors other than the human eye.
1.1.1 List of test methods included in this guide: 2.1 ASTM Standards:
1.1.1.1 Becke line (method of central illumination),
E167 Practice for Goniophotometry of Objects and Materi-
1.1.1.2 Apparent depth of microscope focus (the method of als (Withdrawn 2005)
the Duc de Chaulnes),
E456 Terminology Relating to Quality and Statistics
1.1.1.3 Critical Angle Refractometers (Abbe type and Pul-
3. Terminology
frich type),
1.1.1.4 Metricon system,
3.1 Definitions:
1.1.1.5 Vee-block refractometers,
3.1.1 dispersion, n—the physical phenomenon of the varia-
1.1.1.6 Prism spectrometer, and
tion of refractive index with wavelength.
1.1.1.7 Specular reflectance.
3.1.1.1 Discussion—The term, “dispersion,” is commonly
1.1.2 Test methods presented by name only (see Annex A1):
used in lieu of the more complete expression, “reciprocal
1.1.2.1 Immersion refractometers,
relative partial dispersion.” A dispersion-number can be de-
1.1.2.2 Interferometry,
fined to represent the refractive index as a function of wave-
1.1.2.3 Ellipsometry, and
length over a selected wavelength-range; that is, it is a
1.1.2.4 Method of oblique illumination.
combined measure of both the amount that the index changes
and the non-linearity of the index versus wavelength relation-
ship.
This guide is under the jurisdiction of ASTM Committee C14 on Glass and
Glass Products and is the direct responsibility of Subcommittee C14.11 on Optical
Properties. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved July 1, 2023. Published July 2023. Originally approved contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
in 2006. Last previous edition approved in 2018 as C1648 – 12 (2018). DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/C1648-12R23. the ASTM website.
2 4
Metricon is a trademark of Metricon Corporation 12 North Main Street, P.O. The last approved version of this historical standard is referenced on
Box 63, Pennington, New Jersey 08534. www.astm.org.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1648 − 12 (2023)
A
TABLE 1 Spectral Lines for Measurement of Refractive Index
Fraunhofer Line A’ C C’ D d e F F’ g G’ h
Element K H Cd Na He Hg H Cd Hg H Hg
B C D D
Wavelength Nanometers 786.2 656.3 643.8 589.3 587.6 546.1 486.1 480.0 435.8 434.0 404.7
A
From Ref (1).
B
A later reference (identification not available) lists 789.9 nm for the potassium A’ line, although referring to Ref (1). The Handbook of Chemistry and Physics lists 789.9 nm
as a very strong line, and it does not list a line at 786.2 nm at all.
C
The wavelength of the corresponding deuterium line is 656.0 nm.
D
The two cadmium lines have been recognized for refractometry since Ref (1) was published.
3.1.2 resolution, n—as expressed in power of 10, a com- parts of the spectrum might be used when designing more
monly used term used to express the accuracy of a test method complex optical systems. For most glasses, dispersion in-
in terms of the decimal place of the last reliably measured digit creases with increasing refractive index. For the purposes of
of the refractive index which is expressed as the negative this standard, it is sufficient to describe only two reciprocal
power of 10. As an example, if the last reliably measured digit relative partial dispersions that are commonly used for char-
is in the fifth decimal place, the method would be designated a acterizing glasses. The longest established practice has been to
-5
10 method. cite the Abbe-number (or Abbe ν-value), calculated by:
3.2 Symbols: n = index of refraction ν 5 n 2 1 / n 2 n (1)
~ ! ~ !
D D F C
ν = Abbe-number; a representation of particular relative
where v is defined in 3.2 and n , n , and n are the indices
D D F C
partial dispersions
of refraction at the emission lines defined in 3.2.
ν = Abbe-number determined with spectral lines D, C,
D
and F
4.2.1 Some modern usage specifies the use of the mercury
ν = Abbe-number determined with spectral lines e, C', e-line, and the cadmium C' and F' lines. These three lines are
e
and F'
obtained with a single spectral lamp.
D = the spectral emission line of the sodium doublet at
ν 5 n 2 1 / n 2 n (2)
~ ! ~ !
e e F' C'
nominally 589.3 nm (which is the mid-point of the doublet that
has lines at 589.0 nm and 589.6 nm)
where v is defined in 3.2 and n , n , and n are the indices
e e F' C'
C = the spectral emission line of hydrogen at 656.3 nm of refraction at the emission lines defined in 3.2.
F = the spectral emission line of hydrogen at 486.1 nm
4.2.2 A consequence of the defining equations (Eq 1 and 2)
e = the spectral emission line of mercury at 546.1 nm
is that smaller ν-values correspond to larger dispersions. For
C' = the spectral emission line of cadmium at 643.8 nm
ν-values accurate to 1 % to 4 %, index measurements must be
F' = the spectral emission line of cadmium at 480.0 nm
-4
accurate to 1×10 ; therefore, citing ν-values from less accurate
test methods might not be useful.
4. Significance and Use
NOTE 1—For lens-design, some computer ray-tracing programs use
4.1 Measurement—The refractive index at any wavelength
data directly from the tabulation of refractive indices over the full
of a piece of homogeneous glass is a function, primarily, of its
wavelength range of measurement.
composition, and secondarily, of its state of annealing. The
NOTE 2—Because smaller ν-values represent larger physical
index of a glass can be altered over a range of up to dispersions, the term constringence is used in some texts instead of
-4
dispersion.
1×10 (that is, 1 in the fourth decimal place) by the changing
of an annealing schedule. This is a critical consideration for
5. Precision, Bias, and Accuracy (see Terminology E456)
optical glasses, that is, glasses intended for use in high
performance optical instruments where the required value of an 5.1 Precision—The precision of a method is affected by
-6
index can be as exact as 1×10 . Compensation for minor several of its aspects which vary among methods. One aspect
variations of composition are made by controlled rates of is the ability of the operator to repeat a setting on the observed
annealing for such optical glasses; therefore, the ability to optical indicator that is characteristic of the method. Another
measure index to six decimal places can be a necessity; aspect is the repeatability of the coincidence of the measure-
however, for most commercial and experimental glasses, ment scale of the instrument and the optical indicator (magni-
standard annealing schedules appropriate to each are used to tude of dead-band or backlash); this, too, varies among
limit internal stress and less rigorous methods of test for methods. A third aspect is the repeatability of the operator’s
refractive index are usually adequate. The refractive indices of reading of the measurement scale. Usually, determinations for
-4
glass ophthalmic lens pressings are held to 5×10 because the a single test specimen and for the reference piece should be
tools used for generating the figures of ophthalmic lenses are repeated several times and the resulting scale readings aver-
made to produce curvatures that are related to specific indices aged after discarding any obvious outliers.
of refraction of the lens materials.
5.2 Bias (Systematic Error):
4.2 Dispersion—Dispersion-values aid optical designers in 5.2.1 Absolute Methods—Two of the test methods are abso-
their selection of glasses (Note 1). Each relative partial lute; the others are comparison methods. The absolute methods
dispersion-number is calculated for a particular set of three are the prism spectrometer and the apparent depth of micro-
wavelengths, and several such numbers, representing different scope focus. These yield measures of refractive index of the
C1648 − 12 (2023)
specimen in air. In the case of the prism spectrometer, when TEST METHODS
-6
used for determinations of 1×10 , correction to the index in
6. Becke Line (Method of Central Illumination)
vacuum (the intrinsic property of the material) can be calcu-
lated from the known index of air, given its temperature, 6.1 Summary of the Method—Not-too-finely ground par-
pressure, and relative humidity. The accuracy of the apparent ticles of the glass for testing are immersed in a calibrated
depth method is too poor for correction to vacuum to be refractive index oil and are examined with a microscope of
meaningful. Bias of the prism spectrometer depends upon the moderate magnification. With a particle in focus, if the indices
accuracy of its divided circle. The bias of an index determina- of the oil and the glass match exactly, the particle is not seen;
tion must not be greater than one-half of the least count of no boundary between oil and glass is visible. If the indices
differ, a boundary is seen as a thin, dark line at the boundary of
reading the scale of the divided circle. For a spectrometer
-6
capable of yielding index values accurate to 1×10 , the bias the particle with either the particle or the oil appearing lighter.
-7
The line appears darker as the indices differ more; however,
must be not greater than 5×10 . Bias of the apparent depth
method depends on the accuracy of the device for measuring which material has the higher index is not indicated. When the
focal plane of the microscope is moved above or below the
the displacement of the microscope stage; it is usually appre-
plane of the particle (usually by lowering or elevating the stage
ciable smaller than the precision of the measurement, as
of the microscope), one side of the boundary appears lighter
explained in 7.6.
and the other side appears darker than the average brightness of
5.2.2 Comparison Methods—All of the comparison meth-
the field. When the focus is above the plane of the glass
ods rely upon using a reference material, the index of which is
particle, a bright line next to the boundary appears in the
known to an accuracy that is greater than what can be achieved
medium of higher index. This is the “Becke line”; conversely,
by the measurements of the given method itself; therefore, the
when the focus is below the plane of the particle, the bright line
bias of these methods is the uncertainty of the specified
appears in the medium of lower index. Successive changes of
refractive index of the reference material, provided that the
oil, using new glass particles, lead by trial and error to a
instrument’s scale is linear over the range within which the
bracketing of the index of the particle between the pair of oils
test-specimen and the reference are measured. The bias intro-
that match most closely (or to an exact match). Visual
duced by non-linearity of the scale can be compensated by
interpolation can provide resolution to about one fourth of the
calibrating the scale over its range with reference pieces having
difference between the indices of the two oils. The physical
indices that are distributed over the range of the scale. A table
principle underlying the method is that of total internal
of scale-corrections can be made for ready reference, or a
reflection at the boundary, within the medium of higher index.
computer program can be used; using this, the scale reading for
This is illustrated by a ray diagram, Fig. 1(a). Visual appear-
a single reference piece is entered and then corrected indices
ances are illustrated in Fig. 1(b), Fig. 1(c), and Fig. 1(d), where
are generated for each scale reading made for a set of test
different densities of cross-hatching indicate darker parts of the
specimens. For a single measurement, scale correction can be
field of view. Although calibrated indices are provided for the
made by first measuring the test specimen and then measuring
C- and F-lines, enabling an estimate of a dispersion-value, it
the calibrated reference piece that has the nearest index. In this
must be taken not to be very accurate.
case, the scale is corrected only in the vicinity where the
readings are made. 6.2 Advantages and Limitations—This method uses the
smallest amount of specimen-material and it has the simplest
5.2.3 Test Specimen—Deviations of a test specimen from its
-6
and least expensive method of sample-preparation. Costs of
ideal configuration can contribute a bias. For 1×10
apparatus and materials, too, are moderate, as is the time
refractometry, specimen preparation must be of the highest
needed to make a determination; however, the accuracy of the
order and specimens are tested for acceptability for use. Bias
-4
method is limited to about 5×10 (index-values are less
introduced by a test specimen varies in its manifestation with
accurate for n < 1.40 and n > 1.70).
the type of test method and nature of the deviation from ideal.
NOTE 4—A related test method, the method of oblique illumination, is
This consideration is addressed in the descriptions of indi-
described in Annex A1.
vidual test methods.
NOTE 5—Because the test specimen is very small, the Becke line
method can be used to determine the refractive index of highly absorbing
5.3 Accuracy—The limiting accuracies of the several test
glasses. For example, for a 2 mm thick piece of Corning-Kopp color filter
methods are given. The operator must estimate whether and
-4
CS 7-58, the maximum spectral transmittance is about 1×10 (optical
how much a given test measurement deviates from that limit.
density 4.0); it occurs near 589 nm. Its refractive index was determined to
-3
The estimate should take into account the observed uncertainty 1×10 by the Becke line method. Appreciably higher absorption can result
in there being too little distinction when the indices of specimen and liquid
of identifying where to set on the optical indicator (see 7.6, for
are nearly alike. In this case, the bracketing liquids that can be identified
example) as well as the precision of such settings. Specific
will be more widely separated. Use the mean of their given indices and
considerations are given in the descriptions of the test methods.
assign an appropriately larger uncertainty to the result.
NOTE 3—The Subcommittee did not conduct an Inter-laboratory Study
6.3 Apparatus and Materials:
(as normally required) to quantify the Precision and Bias of Methods
6.3.1 Microscope—Use a microscope having a total magni-
discussed in this Standard. The cited accuracies of the test methods are
based on experience. fication of at least 80× that has a sub-stage condenser with a
C1648 − 12 (2023)
(a) ray diagram showing the principle of the method, n < n ; (b) appearance of Becke lines for specimens of higher (H) and lower (L) refractive index than that of the
1 2
immersion liquid with the microscope-focus above the plane of the specimen-particles; (c) in the plane of the particles; (d) below the plane of the particles
FIG. 1 Becke Line
variable-aperture iris diaphragm. (A 10× objective lens and a Partial sets, by preset groupings or by custom selections, can be
10× ocular are very satisfactory.) purchased according to particular need. The label of each bottle
6.3.2 Microscope Slides and Cover Glasses—Use standard has the index for the sodium D-line at 25 °C, standardized to
-4
glass microscope slides, 1×3-in., 1 mm thick, and microscope 2×10 , the temperature coefficient of index, and the indices for
cover glasses, 18 mm (preferred) or 22 mm and 0.35 mm thick the hydrogen C and F-lines. Liquids with indices above 1.70
(#1 ⁄2). require special handling, as taught by the manufacturer. The
6.3.3 Bandpass Filters—Narrow spectral bandpass filters, oils are supplied in 7.4-cc ( ⁄4 fl oz) bottles; the caps have small
about 1 nm FWHM (full width at half maximum glass rods for transfer of fluid by the drop. The refractive
transmittance), should be used (measurement with white light indices of the oils depend on their temperature; therefore, store
reduces the accuracy of a result). These can be commercial the oils at room temperature and measure the temperature at the
interference filters. Owing to the bandwidth of about 10 nm, time of testing. Temperature-corrections of the indices of the
the wavelengths of the transmittance maxima of the filters need oils must be made.
not fall at exactly the wavelengths of the spectral lines that are
NOTE 6—“Standardized to” is the manufacturer’s statement of the
specified for determining dispersion-numbers. For the Abbe
-4
accuracy of the stated index of n at 25 °C. Standardization to 2×10 is
D
ν-value, standard interference filters with nominal peak wave-
for the range 1.300 to 1.700. Larger tolerances are specified for lower and
lengths of 490 nm, 590 nm, and 650 nm or 660 nm would work
higher range oils.
well. The filter should be mounted close to the substage
6.3.5 Mortar and Pestle—A small mortar and pestle of agate
condenser assembly. This will avoid focusing dirt or surface
or of a hard ceramic is used to prepare the specimens for
defects of the filter onto the plane of the specimen.
observation.
6.3.4 Calibrated Immersion Oils—Sets of calibrated index
6.3.6 Thermometer—A thermometer that is sensitive and
oils are available with indices over the range 1.300 to 2.31.
accurate to 0.5 °C is needed.
5 6.4 Hazards—The immersion oils are somewhat toxic. They
Cargille Laboratories, Inc., 55 Commerce Road, Cedar Grove, NJ 07009-1280,
Tel. 973-239-6633, www.cargille.com should be used in a well ventilated space, and contact with the
C1648 − 12 (2023)
skin should be avoided. The latter is particularly important for tion”) of index (that is, the accuracy of the index) of the oils of
the high index liquids (n > 1.70). Manufacturer’s guidelines a set. Manufacturer’s instructions must be followed to preserve
should be followed. the integrity of accuracy. Cross-contamination of the applicator
rods must be avoided. Bottles must be capped except for the
6.5 Specimen Preparation—Use a small piece of the glass to
brief time that a transfer of liquid is being made.
be tested. Clean it with alcohol and water (or other solvent, if
necessary). Rinse it with water and dry it with a tissue. One or
7. Apparent Depth of Microscope Focus (the Duc de
two cubic millimetres will be more than enough for testing
Chaulnes’ Image Displacement Method)
with a dozen or so oils; therefore, enough to complete a test,
7.1 Summary of the Method—This method has poor accu-
even of an initially completely unknown sample. Put the
racy; for example, about 0.05 for a glass with n = 2.00;
sample into the mortar and crush it into small pieces by
however, Miller (2) describes technique and calculation that
pressing down with the pestle. Use a rocking motion and do not
can provide accuracy of 0.002 for a glass with n = 1.50. The
slide the pestle against the mortar as specimens for measure-
accuracy would be poorer for higher index glasses. The utility
ment should not be too small. A text specifies that they should
of the method lies in the relative ease of specimen-preparation
pass through a 100-mesh sieve and be held back by a 170-mesh
and in its convenience for a quick test of higher index glasses
screen; however, screening is not necessary: the appropriate
(n > 1.70) when higher index calibrated oils are not at hand or
size will be learned by a few trials.
are not wanted to be used; therefore, it can be a useful tool
6.6 Procedure—Transfer about 10 particles of glass to the
where experimental melting of higher index glasses is being
microscope slide using a spatula with a small tip. Three piles
done and quick results are desired. Because of the poor
can be placed on a slide, spaced about 20 mm apart, to speed
accuracy, the method is not suitable for determining dispersion.
the course of measurements. Spread the particles over an area
The principle of the method is illustrated in Fig. 2(a) and Fig.
about 10 mm diameter and remove any exceptionally large
2(b). The specimen is a flat parallel-sided piece of glass, both
particles. Lay a cover slip on the spread and dispense one drop
sides polished. Marks are placed on top and bottom surfaces
of a calibrated index oil by touching the tip of the rod to the
and the piece is examined with a moderate-power microscope.
edge of the cover slip and the surface of the slide. (Second or
The mark on the top surface is brought into focus and an index
third drops, applied to other edges, might be needed for
of the elevation of the specimen relative to the objective lens is
adequate immersion of the particles.) Capillary action will
recorded. Then, the mark on the bottom surface is brought into
draw the liquid in and immerse the glass particles. Place the
focus and the index of the elevation of the specimen is again
slide on the stage of the microscope. Close the iris diaphragm
recorded, thus providing a measure of the displacement of the
appreciably. Bring a particle into focus and adjust the iris
specimen relative to the position of the objective lens. The
diagram and the focus until the boundary between particle and
simplified, often used, but rather inaccurate calculation of the
oil is sharp (Fig. 1(c)). Note the darkness and breadth of the
refractive index of the glass n is given by:
g
particle-oil boundary for estimating whether a small or a large
n 't/d (3)
g
change of index for the next oil is needed. Raise the focal plane
of the microscope above the plane of the particle while
where:
observing the formation of the bright Becke line and its motion
t = thickness of the specimen, and
into one medium, whether glass or oil. Repeat these observa-
d = displacement of the stage of the microscope.
tions for several particles and act according to the indication of
7.1.1 The derivation of Eq 3 and explanation of the sources
the majority. For the next trial, choose an oil with index closer
of error are given in Appendix X1.
to that of the glass. Repeat the procedure until a match is
achieved or until the two closest (bracketing) oils are found. If
7.2 Apparatus and Materials:
it is desired to have an estimate of the dispersion of the glass, 7.2.1 Microscope—The microscope should have a total
repeat the procedure with bandpass filters for the C and F-lines.
magnification of about 100× and the objective lens should
provide about 10× of that. (See Appendix X1 for discussion of
6.7 Calculation—Estimate the index by interpolating be-
effect of magnification of the objective lens.) The stage should
tween the indices of the bracketing oils using relative contrasts
have provision for fine adjustment of its elevation.
of the boundary when the particle is in focus. The estimate can
7.2.2 Marker—Use a felt-tipped marker capable of making
be as good as one-fourth of the step of index between the two
a very thin (in the thickness dimension) line on the polished
oils. The estimate must also be whether to assign the exact
glass surface.
index of one oil (for a close match) or to assign the value of the
7.2.3 Narrow Bandpass Filter—Use a narrow bandpass
nearest quarter-step. Multiply the difference between 25 °C and
filter, such as described in 6.3.3, chosen for either n or n .
D e
the temperature of the oil (that is, room temperature) by the
7.2.4 LVDT or Dial Gauge—Either a linearly variable
temperature coefficient of index-variation and add (algebra-
differential transformer (LVDT) or a dial gauge is used to
ically) to obtain the correct index. Because the rate of variation
measure the vertical displacement of the stage of the micro-
of index is very much larger for the oils than it is for glass, no
scope relative to the objective lens. Consult the manufacturer’s
adjustment is needed for the glass.
6.8 Precision and Bias—Precision can be slightly better
than one-fourth of the size of the step between adjacent oils of
The boldface numbers in parentheses refer to the list of references at the end of
a set. Bias is limited to the stated adjustment (“standardiza- this standard.
C1648 − 12 (2023)
(a) focus on mark on top of specimen; (b) focus on mark on bottom surface of the specimen, with ray diagram and definition of symbols
FIG. 2 Apparent Depth of Microscope Focus
instructions for mounting the LVDT and for measuring dis- 7.4 Procedure—Position the specimen on the stage such that
placement with it. A dial gauge mounted on a stand can be the axis where the marks cross is at the center of the field of
placed with its axis vertical and the tip of its shaft on and near view. Focus onto the mark on the top surface and record the
the edge of the stage of the microscope. The dial gauge should elevation of the stage as indicated by the LVDT or dial gauge.
be divided into 0.01 mm markings, spaced such that interpo- Repeat at least five times; eliminate obvious outliers; and
lation to 0.002 mm can be made. The dial gauge should be calculate the average of several readings. Raise the stage to
tapped gently at each setting and an electrical vibrator (buzzer) bring the mark on the bottom surface into focus and record the
should be fastened to the base of the mounting of the dial elevation, repeating as above. Tap the dial gauge or use the
gauge. These are to overcome sticking of the gauge which vibrator to home-in the dial gauge at each setting.
occurs because motion in adjusting the focus is very slow. A
7.5 Calculation—Use Eq 3 for a first approximation of the
step-down transformer and momentary contact switch are
index. Use Eq 4 as a refinement that eliminates the error from
needed for operating the buzzer.
replacing tangents of angles with their sines (see Appendix
7.2.5 Micrometer Caliper—A micrometer caliper capable of
X1).
being read to 0.002 mm by interpolation must be used for
2 2 2 1/2
n 5 t/d 2 NA t/d 2 1 (4)
$~ ! @~ ! #%
g
measuring the thickness of the specimen.
where:
7.3 Specimen Preparation—The cross-section of the speci-
men should be large enough for convenient grinding and
NA = numerical aperture of the objective lens,
polishing flat and parallel surfaces: 21 cm by 2 cm (2 cm t = thickness of the specimen, and
d = displacement of the stage of the microscope.
square) or diameter is satisfactory. Measure the thickness of the
specimen to an accuracy of 0.002 mm. Clean the surfaces with NOTE 7—The significance of using this correct formula is illustrated by
these examples. (1) For t/d = 1.60, by Eq 3, n = 1.6, and by Eq 4,
g
alcohol and distilled water. Mark a line on one surface, near the
n = 1.50; (2) for t/d = 2.19, by Eq 3, n = 2.19, and by Eq 4, n = 2.00.
g g g
center of the piece, and then a line on the other surface such
that an X is seen when viewed perpendicularly. Make the mark 7.6 Precision and Bias—Precision must be determined by
as thin as possible but still easily seen with the microscope. the operator for each test, as it can vary with thickness of the
C1648 − 12 (2023)
FIG. 3 Principle of Critical Angle Refractometers
specimen and its refractive index, and on the ability to repeat specimen with an optically flat polished surface is held onto the
the focusing on a mark. Precision can be improved by making prism-face by capillary attraction of a coupling liquid which
several replicate measurements and by a using a microscope must have a higher index than that of the glass. The interface
objective lens with higher magnification (Note 8). Also, for a is illuminated by a spectral lamp such that rays fall at grazing
lens of given magnification, precision can be greater with an
incidence along the interface and at a small range angles above
objective lens that has a higher numerical aperture. The grazing. They enter the glass through a polished face that is
accuracy of determining the displacement is better with a
perpendicular to the contact face. The back face of the prism is
calibrated LVDT than with a dial gauge. Bias depends on the viewed with a simple telescope that focuses emerging rays onto
accuracy of the gauges used. Lack of parallelism of the faces of
cross hairs; these are viewed through an eyepiece. The light
the test specimen will introduce a small bias. Bias will that is incident at grazing incidence enters the prism at the
ordinarily be smaller than the errors from imprecision of
critical angle θ given by:
c
setting the focus.
θ 5 sin n /n (5)
~ !
c g p
NOTE 8—A lens of higher magnification will have a shorter working
distance; therefore, the thickness of the specimen will affect how high a
where:
magnification lens can be used. See Appendix X1.
n and n = refractive indices of the glass specimen and the
g p
measurement prism, respectively, for the wave-
8. Critical Angle Refractometers (Abbe Type and
length of the spectral line.
Pulfrich Type)
8.1 Summary of the Method—The principle of critical angle 8.1.1 Light incident from above grazing incidence enters the
refractometry is illustrated in Fig. 3. It was first realized by prism at angles less than the critical angle. Thus, the field
Abbe. The modification by Pulfrich is the (near-) linearization viewed through the telescope appears to be divided by a
of the measurement scale of the refractometer as a function of more-or-less sharp boundary, light on one side and dark on the
the index of the test specimen. In order to cover a very wide other. The prism is rotated to bring the demarcation line into
range of indices, measurement prisms having different indices coincidence with the cross hairs. A scale related to the angular
are used. The index of the measurement prism must be higher rotation of the prism (or of a mirror located between the prism
than that of the test specimen. Excellence in the preparation of and the telescope) is read and converted to the refractive index
a test specimen is critical in order to realize accuracies in the of the glass by reference to tables provided by the manufac-
fifth decimal place (Note 9). Straat and Forest (3) analyze turer. Before measuring new test specimens, the scale is first
accuracy requirements for fifth decimal place refractometry. checked with one or more reference specimens of excellent
Tilton (4) provides valuable instruction as well. A glass optical finish and known refractive index; if needed, either an
C1648 − 12 (2023)
by noting the precision of setting on a somewhat diffuse demarcation line.
adjustment is made to the scale by shifting the cross hair
slightly, or by rotating the prism relative to the scale if need be,
8.4 Procedure—Start by cleaning the faces of the prism and
in accordance with the manufacturer’s instructions. If the error
the specimen meticulously, using a soft tissue wetted with
of the scale reading is small, it may be used as a correction
alcohol or xylene. Do not use acetone or similar solvents. Dry
without making mechanical adjustments. See 5.2.2 concerning
the surfaces and be certain that no grit, fine dust, or lint remain.
scale corrections
Repeat this cleaning each time a new test piece or a calibrated
NOTE 9—The Bausch & Lomb Precision Refractometer, a Pulfrich-type
reference piece is to be mounted. Put a small drop of coupling
instrument, is no longer manufactured commercially; however, a great
liquid on the polished face of the test specimen and press the
many of these instruments are still in use. The Reference Manual provided
specimen onto the prism. Squeeze the liquid out and remove
with the Bausch & Lomb Precision Refractometers is a very good guide
any excess with a tissue. Minimize sliding of the specimen on
for the preparation of glass specimens and for measurement procedures
(although it is obsolete in its information on spectral lamps).
the face of the prism: scratching of a prism-face severely
affects the sharpness of the edge between dark and bright areas
8.2 Apparatus and Materials:
of the field viewed by the telescope. Be especially careful to
8.2.1 Refractometer—A commercial Abbe or Pulfrich re-
remove all liquid at the edge of the specimen that is toward the
fractometer with calibrated reference test pieces.
light source. Adjust the lamp to illuminate the full end of the
8.2.2 Coupling Liquids—The B&L instruction manual
specimen. A large and diffuse source is desirable. The B&L
specifies the requirements for the coupling liquid that attaches
Precision Refractometer has an auxiliary lens in the telescope
the test specimen to the measurement prism: “The first criterion
tube. When rotated into place, the specimen-prism interface is
for choice of liquid is that its index be greater than that of the
in focus, and interference fringes between the prism and the
sample being read. The second is that its index be fairly well
specimen can be examined. “It is helpful to see a few of these
removed from that of either prism or sample.” The index of the
fringes, indicating good mounting.” (4). Producing a slight
liquid may lie between those of the two glasses, or it may be
wedge in the liquid is recommended. Fringes running parallel
higher than that of the prism, but the intermediate choice is
to the direction of the light beam indicate a wedge in the
preferable. A part of the procedure is to view the interference
vertical direction, and this will not affect the indicated refrac-
fringes set up within the liquid layer between the two glasses;
tive index; however, vertical fringes indicate a wedge in the
the second criterion is intended to ensure good visibility of the
direction of that of the light beam. This can introduce an error
fringes. Three liquids suggested in the B&L manual are
of the indicated index. “For viewing fringes in the exit pupil of
Methylene Iodide, n = 1.74; 1-Bromo-Naphthalene,
D 1
the telescope, the tolerance is always ⁄3 fringe of yellow light”
n = 1.66; and Anise Oil, n = 1.55. Other liquids can be
-5
D D
for accuracy of 1×10 (4) . When the specimen is suitably
selected from commercial sets of calibrated oils.
mounted, rotate the measurement prism to bring the demarca-
8.2.3 Spectral Lamps—Spectral lamps of several elements
tion line into view and center it on the cross hairs. If the line is
or combinations of elements are available commercially. A
not sharp, make the best estimate possible of the middle of the
mercury-cadmium lamp provides three spectral lines (F', e, and
transition region and set there. Diffuse demarcation lines result
C'). Provided that prism indices are known, measurements can
from a scratched prism-face, from a liquid wedge, from
be made through the visible spectrum from Hg, 404.7 nm to K
inhomogeneities (scatterers) in the specimen, and from a
(Potassium), 769.9 nm. Table 1 lists eleven spectral lines
specimen surface that is not flat enough (which introduces a
recommended for refractometry (report of the International
liquid wedge). Read the scale and translate the reading into a
Commission of Optics (1)). When using dim lines or those near
value of refractive index. Always clean and dry the face of the
the ends of the visual range, it may be helpful to use an
measurement prism at the end of the measuring session. Place
isolating filter to reduce stray brightness in the field of view.
a double-layer of dry tissue on the surface and close the
“illuminating prism” over it.
8.3 Specimen Preparation—Dimensions of a specimen are
not critical. A typical size is 1 cm wide by 2 cm long by 2 mm
8.5 Precision and Bias—Precision depends on the sharpness
to 3 mm thick. Pieces as small as one-half these values in width
of the demarcation line and how well the operator can reset to
and length can be used. Two surfaces, a large flat and an end,
that line. With a good line, the precision can be as good as the
must be polished, nearly optically flat, and nearly perpendicu-
least count that the scale can be read (Note 11). Several
lar. Gunter and Kobeissi (5) show that the angle should be 90°
repetitions of the setting should be made, reading the scale for
or obtuse up to 91°. The other surfaces may be matte. The
each and averaging for the best estimate of the correct setting.
flatness of the large face should be within one fringe of green
Bias depends upon how well the instrument has been adjusted
light, tested with a small optical flat (see Note 10 and 8.4).
with the calibrated reference pieces. In principle, accuracy to
Instead of a polished end, a fine matte end-face may be used at -5
1×10 is possible, but claimed limiting accuracies of commer-
-5
the cost of the loss of some light (4). Specimen preparation
cial instruments are 3×10 (a Pulfrich refractometer) and
may be accomplished more easily this way. It is imperative that -5
4×10 (an Abbe refractometer) for measured indices of glass
the edge of intersection between the polished face and the end
near 1.5 (Note 12).
toward the light source be sharp in order to achieve the limiting
NOTE 11—“Least count” means the limit of readability with visual
accuracy of a given instrument (Note 10).
interpolation between adjacent scale divisions. This is about one fifth of a
division of the scale of the B&L Precision refractometer.
NOTE 10—This is best accomplished with pitch polishing. Felt polish-
ing tends to roll the surface at the edges, and flatness to three fringes is NOTE 12—Many commercial Abbe-type instruments are intended only
what is customarily obtained, but care is required even for this. The effect for measuring liquids; their accuracies are not as good. For measuring
is to reduce the accuracy of a measurement slightly. This can be estimated glass, a commercial instrument should be specified as suitable for that
C1648 − 12 (2023)
FIG. 4 (a) Principle of Metricon System, (b) Detector Response vs. Rotation Angle (θ )
i
purpose and its accuracy should be stated. thin surface skin layers which result from tin diffusion into the float side
of glasses. In some cases, refractive index profiles vs. depth can even be
9. The Metricon System
determined for float glass skin layers.
9.1 Summary of the Method—The Metricon system is also
9.2 Apparatus and Materials—Commercial Metricon sys-
based on critical angle refractometry and Eq 5 applies. The
tem with one or more lasers and prism suitable to the index
principle of the method, which involves rotating the sample
range of interest. Standard prisms cover a wide index range
and a high index prism with respect to a stationary laser, is
(for example, from 1.0 to 1.8 or 1.6 to 2.45) and prisms to
illustrated in Fig. 4a. Differing from the Abbe-type
cover different index ranges can be interchanged in approxi-
refractometers, illumination of the interface between the test
mately one minute.
specimen and the measurement prism is from within the prism.
9.2.1 Calibration—Referring to Eq 5 and Fig. 4a, it can be
-4
The accuracy is about 1–2 × 10 contingent on using a
seen that accuracy in determining n depends only on accurate
g
reference standard (for example, fused silica or precision
knowledge of the critical angle (θ ) and the prism index (n ).
c p
optical glass) with refractive index that is known to a higher
Using auto-collimation techniques to measure the incident
degree of accuracy. The lasers used have small (~1 mr)
angle of the laser beam on the prism, with reasonable sample
divergences and small diameter (~1 mm) beams. Measure-
surface quality θ can be determined to a precision correspond-
c
ments are made at discrete wavelengths but the system can be -4
ing to an index accuracy of ~1 x 10 . However, since very high
configured with up to five lasers chosen from a list of a dozen
index prisms are required for this technique (typical prism
or so standard lasers with wavelength ranging from 405 nm to
indices range from ~1.95 to 3.5) accurate index data for prism
1550 nm. The system generates a Cauchy curve of index vs.
materials are not available and there can even be some index
wavelength when index at three or more wavelengths is
variation from prism to prism of the same material.
measured and it can also be configured to accept user supplied
Consequently, prism index at each measurement wavelength
lasers. Advantages of the system are: (1) specimen preparation
must be determined by using the system to measure the index
is relatively easy (2) index matching fluids are not required; (3)
of a reference standard whose index is known to an accuracy of
measurements are possible over a very wide range of index – -5
5 × 10 or better (a series of such standards made from fused
from 1.0 to ~2.65 in the visible and up to 3.35 in the near
silica, NIST SRM’s, or precision high index glasses from
infrared (4) an option (which heats both the back of the sample
manufacturers such as Schott, Hoya, or Ohara are available
and the prism to the same temperature) is available to measure 2
from Metricon to cover the index range from 1.46 to 2.10).
index vs. temperature (dn/dT) over the range 25–200 C. The
The prism index is then corrected to the value which correctly
polished face of the test specimen is pressed against the surface
measures the index of the standard. Calibration, however, is a
of the measurement prism and held there by a pneumatic
one-time process; once calibrated, measurements are extremely
piston. To minimize operator subjectivity, the measurement is
stable over months or years since the refractive index of the
carried out under computer control and the identification of the
prism does not change.
critical angle is determined automatically from the plot of
9.3 Specimen Preparation—The specimen must have one
detector response (light intensity reflected from the sample
polished surface, and the back surface can be ground or saw cut
prism interface) vs. angle of incidence (Fig. 4b). Scanning the
and nonparallel by up to ~5°. The technique is relatively
angle of incidence of the laser beam on the prism-specimen
forgiving of less than perfect optical polish although poor
interface is by a stepper motor driven
...