ASTM C1648-12(2018)

Standard Guide for Choosing a Method for Determining the Index of Refraction and Dispersion of Glass

SIGNIFICANCE AND USE
4.1 Measurement—The refractive index at any wavelength of a piece of homogeneous glass is a function, primarily, of its composition, and secondarily, of its state of annealing. The index of a glass can be altered over a range of up to 1×10-4 (that is, 1 in the fourth decimal place) by the changing of an annealing schedule. This is a critical consideration for optical glasses, that is, glasses intended for use in high performance optical instruments where the required value of an index can be as exact as 1×10-6. Compensation for minor variations of composition are made by controlled rates of annealing for such optical glasses; therefore, the ability to measure index to six decimal places can be a necessity; however, for most commercial and experimental glasses, standard annealing schedules appropriate to each are used to limit internal stress and less rigorous methods of test for refractive index are usually adequate. The refractive indices of glass ophthalmic lens pressings are held to 5×10-4 because the tools used for generating the figures of ophthalmic lenses are made to produce curvatures that are related to specific indices of refraction of the lens materials.  
4.2 Dispersion—Dispersion-values aid optical designers in their selection of glasses (Note 1). Each relative partial dispersion-number is calculated for a particular set of three wavelengths, and several such numbers, representing different parts of the spectrum might be used when designing more complex optical systems. For most glasses, dispersion increases with increasing refractive index. For the purposes of this standard, it is sufficient to describe only two reciprocal relative partial dispersions that are commonly used for characterizing glasses. The longest established practice has been to cite the Abbe-number (or Abbe ν-value), calculated by:
where vD is defined in 3.2 and nD, nF, and nC are the indices of refraction at the emission lines defined in 3.2.  
4.2.1 Some modern usage sp...
SCOPE
1.1 This guide identifies and describes seven test methods for measuring the index of refraction of glass, with comments relevant to their uses such that an appropriate choice of method can be made. Four additional methods are mentioned by name, and brief descriptive information is given in Annex A1. The choice of a test method will depend upon the accuracy required, the nature of the test specimen that can be provided, the instrumentation available, and (perhaps) the time required for, or the cost of, the analysis. Refractive index is a function of the wavelength of light; therefore, its measurement is made with narrow-bandwidth light. Dispersion is the physical phenomenon of the variation of refractive index with wavelength. The nature of the test-specimen refers to its size, form, and quality of finish, as described in each of the methods herein. The test methods described are mostly for the visible range of wavelengths (approximately 400 to 780 μm); however, some methods can be extended to the ultraviolet and near infrared, using radiation detectors other than the human eye.  
1.1.1 List of test methods included in this guide:
1.1.1.1 Becke line (method of central illumination),
1.1.1.2 Apparent depth of microscope focus (the method of the Duc de Chaulnes),
1.1.1.3 Critical Angle Refractometers (Abbe type and Pulfrich type),
1.1.1.4 Metricon2 system,
1.1.1.5 Vee-block refractometers,
1.1.1.6 Prism spectrometer, and
1.1.1.7 Specular reflectance.  
1.1.2 Test methods presented by name only (see Annex A1):
1.1.2.1 Immersion refractometers,
1.1.2.2 Interferometry,
1.1.2.3 Ellipsometry, and
1.1.2.4 Method of oblique illumination.  
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regul...

General Information

• Status: Historical
• Publication Date: 31-Jul-2018
• ICS: 81.040.30 - Glass products
• Technical Committee: C14 - Glass and Glass Products
• Drafting Committee: C14.11 - Optical Properties

Standards Content (Sample)

NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: C1648 − 12 (Reapproved 2018)
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 to 780 µm); however, some
methods can be extended to the ultraviolet and near infrared,
2. Referenced Documents
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 Aug. 1, 2018. Published August 2018. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 2006. Last previous edition approved in 2012 as C1648 – 12. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/C1648-12R18. 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 (2018)
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 (2018)
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
reading the scale of the divided circle. For a spectrometer differ, a boundary is seen as a thin, dark line at the boundary of
-6
the particle with either the particle or the oil appearing lighter.
capable of yielding index values accurate to 1×10 , the bias
-7
must be not greater than 5×10 . Bias of the apparent depth The line appears darker as the indices differ more; however,
which material has the higher index is not indicated. When the
method depends on the accuracy of the device for measuring
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
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: C1648 − 12 C1648 − 12 (Reapproved 2018)
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
1.1 This guide identifies and describes seven test methods for measuring the index of refraction of glass, with comments
relevant to their uses such that an appropriate choice of method can be made. Four additional methods are mentioned by name,
and brief descriptive information is given in Annex A1. The choice of a test method will depend upon the accuracy required, the
nature of the test specimen that can be provided, the instrumentation available, and (perhaps) the time required for, or the cost of,
the analysis. Refractive index is a function of the wavelength of light; therefore, its measurement is made with narrow-bandwidth
light. Dispersion is the physical phenomenon of the variation of refractive index with wavelength. The nature of the test-specimen
refers to its size, form, and quality of finish, as described in each of the methods herein. The test methods described are mostly
for the visible range of wavelengths (approximately 400 to 780μm);780 μm); however, some methods can be extended to the
ultraviolet and near infrared, using radiation detectors other than the human eye.
1.1.1 List of test methods included in this guide:
1.1.1.1 Becke line (method of central illumination),
1.1.1.2 Apparent depth of microscope focus (the method of the Duc de Chaulnes),
1.1.1.3 Critical Angle Refractometers (Abbe type and Pulfrich type),
1.1.1.4 Metricon system,
1.1.1.5 Vee-block refractometers,
1.1.1.6 Prism spectrometer, and
1.1.1.7 Specular reflectance.
1.1.2 Test methods presented by name only (see Annex A1):
1.1.2.1 Immersion refractometers,
1.1.2.2 Interferometry,
1.1.2.3 Ellipsometry, and
1.1.2.4 Method of oblique illumination.
1.2 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.3 Warning—Refractive index liquids are used in several of the following test methods. Cleaning with organic liquid solvents
also is specified. Degrees of hazard associated with the use of these materials vary with the chemical nature, volatility, and quantity
used. See manufacturer’s literature and general information on hazardous chemicals.
1.4 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.
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.
Current edition approved Oct. 1, 2012Aug. 1, 2018. Published November 2012August 2018. Originally approved in 2006. Last previous edition approved in 20062012
as C1648C1648 – 12.-06. DOI: 10.1520/C1648-12.10.1520/C1648-12R18.
Metricon is a trademark of Metricon Corporation 12 North Main Street, P.O. Box 63, Pennington, New Jersey 08534.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
C1648 − 12 (2018)
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.
2. Referenced Documents
2.1 ASTM Standards:
E167 Practice for Goniophotometry of Objects and Materials (Withdrawn 2005)
E456 Terminology Relating to Quality and Statistics
3. Terminology
3.1 Definitions:
3.1.1 dispersion, n—the physical phenomenon of the variation of refractive index with wavelength.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
The last approved version of this historical standard is referenced on www.astm.org.
3.1.1.1 Discussion—
The term, “dispersion,” is commonly used in lieu of the more complete expression, “reciprocal relative partial dispersion.” A
dispersion-number can be defined to represent the refractive index as a function of wavelength over a selected wavelength-range;
that is, it is a combined measure of both the amount that the index changes and the non-linearity of the index versus wavelength
relationship.
3.1.2 resolution, n—as expressed in power of 10, a commonly used term used to express the accuracy of a test method in terms
of the decimal place of the last reliably measured digit of the refractive index which is expressed as the negative power of 10. As
-5
an example, if the last reliably measured digit is in the fifth decimal place, the method would be designated a 10 method.
3.2 Symbols: n = index of refraction
ν = Abbe-number; a representation of particular relative partial dispersions
ν = Abbe-number determined with spectral lines D,C, and F
D
ν = Abbe-number determined with spectral lines e,C', and F'
e
D = the spectral emission line of the sodium doublet at nominally 589.3 nm (which is the mid-point of the doublet that has lines
at 589.0 nm and 589.6 nm)
C = the spectral emission line of hydrogen at 656.3 nm
F = the spectral emission line of hydrogen at 486.1 nm
e = the spectral emission line of mercury at 546.1 nm
C' = the spectral emission line of cadmium at 643.8 nm
F' = the spectral emission line of cadmium at 480.0 nm
4. Significance and Use
4.1 Measurement—The refractive index at any wavelength of a piece of homogeneous glass is a function, primarily, of its
-4
composition, and secondarily, of its state of annealing. The index of a glass can be altered over a range of up to 1×10 (that is,
1 in the fourth decimal place) by the changing of an annealing schedule. This is a critical consideration for optical glasses, that
-6
is, glasses intended for use in high performance optical instruments where the required value of an index can be as exact as 1×10 .
Compensation for minor variations of composition are made by controlled rates of annealing for such optical glasses; therefore,
the ability to measure index to six decimal places can be a necessity; however, for most commercial and experimental glasses,
standard annealing schedules appropriate to each are used to limit internal stress and less rigorous methods of test for refractive
-4
index are usually adequate. The refractive indices of glass ophthalmic lens pressings are held to 5×10 because the tools used for
generating the figures of ophthalmic lenses are made to produce curvatures that are related to specific indices of refraction of the
lens materials.
4.2 Dispersion—Dispersion-values aid optical designers in their selection of glasses (Note 1). Each relative partial
dispersion-number is calculated for a particular set of three wavelengths, and several such numbers, representing different parts
of the spectrum might be used when designing more complex optical systems. For most glasses, dispersion increases with
C1648 − 12 (2018)
increasing refractive index. For the purposes of this standard, it is sufficient to describe only two reciprocal relative partial
dispersions that are commonly used for characterizing glasses. The longest established practice has been to cite the Abbe-number
(or Abbe ν-value), calculated by:
ν 5 ~n 2 1!/~n 2 n ! (1)
D D F C
where v is defined in 3.2 and n ,n , and n are the indices of refraction at the emission lines defined in 3.2.
D D F C
4.2.1 Some modern usage specifies the use of the mercury e-line, and the cadmium C' and F' lines. These three lines are obtained
with a single spectral lamp.
ν 5 ~n 2 1!/~n 2 n ! (2)
e e F' C'
where v is defined in 3.2 and n ,n , and n are the indices of refraction at the emission lines defined in 3.2.
e e F' C'
4.2.2 A consequence of the defining equations (Eq 1 and 2) is that smaller ν-values correspond to larger dispersions. For
-4
ν-values accurate to 1 to 4 %, index measurements must be accurate to 1×10 ; therefore, citing ν-values from less accurate test
methods might not be useful.
NOTE 1—For lens-design, some computer ray-tracing programs use data directly from the tabulation of refractive indices over the full wavelength range
of measurement.
NOTE 2—Because smaller ν-values represent larger physical dispersions, the term constringence is used in some texts instead of dispersion.
5. Precision, Bias, and Accuracy (see Terminology E456)
5.1 Precision—The precision of a method is affected by several of its aspects which vary among methods. One aspect is the
ability of the operator to repeat a setting on the observed optical indicator that is characteristic of the method. Another aspect is
the repeatability of the coincidence of the measurement scale of the instrument and the optical indicator (magnitude of dead-band
or backlash); this, too, varies among methods. A third aspect is the repeatability of the operator’s reading of the measurement scale.
Usually, determinations for a single test specimen and for the reference piece should be repeated several times and the resulting
scale readings averaged after discarding any obvious outliers.
5.2 Bias (Systematic Error):
5.2.1 Absolute Methods—Two of the test methods are absolute; the others are comparison methods. The absolute methods are
the prism spectrometer and the apparent depth of microscope focus. These yield measures of refractive index of the specimen in
-6
air. In the case of the prism spectrometer, when used for determinations of 1×10 , correction to the index in vacuum (the intrinsic
property of the material) can be calculated from the known index of air, given its temperature, pressure, and relative humidity. The
accuracy of the apparent depth method is too poor for correction to vacuum to be meaningful. Bias of the prism spectrometer
depends upon the accuracy of its divided circle. The bias of an index determination must not be greater than one-half of the least
-6
count of reading the scale of the divided circle. For a spectrometer capable of yielding index values accurate to 1×10 , the bias
-7
must be not greater than 5×10 . Bias of the apparent depth method depends on the accuracy of the device for measuring the
displacement of the microscope stage; it is usually appreciable smaller than the precision of the measurement, as explained in 7.6.
5.2.2 Comparison Methods—All of the comparison methods rely upon using a reference material, the index of which is known
to an accuracy that is greater than what can be achieved by the measurements of the given method itself; therefore, the bias of these
methods is the uncertainty of the specified refractive index of the reference material, provided that the instrument’s scale is linear
over the range within which the test-specimen and the reference are measured. The bias introduced by non-linearity of the scale
can be compensated by calibrating the scale over its range with reference pieces having indices that are distributed over the range
of the scale. A table of scale-corrections can be made for ready reference, or a computer program can be used; using this, the scale
reading for a single reference piece is entered and then corrected indices are generated for each scale reading made for a set of
test specimens. For a single measurement, scale correction can be made by first measuring the test specimen and then measuring
the calibrated reference piece that has the nearest index. In this case, the scale is corrected only in the vicinity where the readings
are made.
-6
5.2.3 Test Specimen—Deviations of a test specimen from its ideal configuration can contribute a bias. For 1×10 refractometry,
specimen preparation must be of the highest order and specimens are tested for acceptability for use. Bias introduced by a test
specimen varies in its manifestation with the type of test method and nature of the deviation from ideal. This consideration is
addressed in the descriptions of individual test methods.
5.3 Accuracy—The limiting accuracies of the several test methods are given. The operator must estimate whether and how much
a given test measurement deviates from that limit. The estimate should take into account the observed uncertainty of identifying
where to set on the optical indicator (see 7.6, for example) as well as the precision of such settings. Specific considerations are
given in the descriptions of the test methods.
NOTE 3—The Subcommittee did not conduct an Inter-laboratory Study (as normally required) to quantify the Precision and Bias of Methods discussed
in this Standard. The cited accuracies of the test methods are based on experience.
C1648 − 12 (2018)
(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
TEST METHODS
6. Becke Line (Method of Central Illumination)
6.1 Summary of the Method—Not-too-finely ground particles of the glass for testing are immersed in a calibrated refractive
index oil and are examined with a microscope of moderate magnification. With a parti
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