Abstract

Five refractive methods and an interferometric method for measuring refractive indices of optical glasses to a precision of several units in the sixth or seventh decimal place are examined. Tables and graphs are presented as aids in evaluating the various methods. Reduction to standard conditions of temperature, pressure, and humidity is also discussed. The minimum deviation method provides greater precision than the autocollimating method for the same precision in angle measurement. The V block, immersion, and critical angle methods, being comparative methods, provide lower precision. A proposed interferometer method shows capability for seventh place accuracy.

© 1968 Optical Society of America

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References

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  1. L. W. Tilton, J. Res. Nat. Bur. Stand. 2, 909 (1929).
  2. L. W. Tilton, J. Res. Nat. Bur. Stand. 6, 59 (1931).
  3. L. W. Tilton, J. Res. Nat. Bur. Stand. 11, 25 (1933).
  4. L. W. Tilton, J. Res. Nat. Bur. Stand. 13, 111 (1934).
    [CrossRef]
  5. L. W. Tilton, J. Res. Nat. Bur. Stand. 14, 393 (1935).
    [CrossRef]
  6. M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 176.
  7. B. Edlén, Metrologia 2, 71 (1966).
    [CrossRef]
  8. R. Penndorf, J. Opt. Soc. Amer. 47, 176 (1957).
    [CrossRef]
  9. F. A. Molby, J. Opt. Soc. Amer. 39, 600 (1949).
    [CrossRef]
  10. J. V. Hughes, J. Sci. Instrum. 18, 234 (1941).
    [CrossRef]
  11. C. A. Faick, B. Fonoroff, J. Res. Nat. Bur. Stand. 32, 67 (1944).
    [CrossRef]
  12. L. W. Tilton, J. Opt. Soc. Amer. 32, 371 (1942).
    [CrossRef]
  13. L. W. Tilton, J. Res. Nat. Bur. Stand. 30, 311 (1943).
    [CrossRef]
  14. H. W. Straat, J. W. Forrest, J. Opt. Soc. Amer. 29, 240 (1939).
    [CrossRef]
  15. Ref. 6, p. 267.
  16. R. W. Ditchburn, Light (Interscience Publishers, Inc., New York, 1963), 2nd ed., p. 346.
  17. T. R. Young, “Achromatic Interferometer for Gage Block Comparison,” Metrology of Gage Blocks, NBS Circular #581 (1957), p. 49.
  18. P. G. Guest, W. M. Simmons, J. Opt. Soc. Amer. 43, 319 (1953).
    [CrossRef]

1966 (1)

B. Edlén, Metrologia 2, 71 (1966).
[CrossRef]

1957 (2)

R. Penndorf, J. Opt. Soc. Amer. 47, 176 (1957).
[CrossRef]

T. R. Young, “Achromatic Interferometer for Gage Block Comparison,” Metrology of Gage Blocks, NBS Circular #581 (1957), p. 49.

1953 (1)

P. G. Guest, W. M. Simmons, J. Opt. Soc. Amer. 43, 319 (1953).
[CrossRef]

1949 (1)

F. A. Molby, J. Opt. Soc. Amer. 39, 600 (1949).
[CrossRef]

1944 (1)

C. A. Faick, B. Fonoroff, J. Res. Nat. Bur. Stand. 32, 67 (1944).
[CrossRef]

1943 (1)

L. W. Tilton, J. Res. Nat. Bur. Stand. 30, 311 (1943).
[CrossRef]

1942 (1)

L. W. Tilton, J. Opt. Soc. Amer. 32, 371 (1942).
[CrossRef]

1941 (1)

J. V. Hughes, J. Sci. Instrum. 18, 234 (1941).
[CrossRef]

1939 (1)

H. W. Straat, J. W. Forrest, J. Opt. Soc. Amer. 29, 240 (1939).
[CrossRef]

1935 (1)

L. W. Tilton, J. Res. Nat. Bur. Stand. 14, 393 (1935).
[CrossRef]

1934 (1)

L. W. Tilton, J. Res. Nat. Bur. Stand. 13, 111 (1934).
[CrossRef]

1933 (1)

L. W. Tilton, J. Res. Nat. Bur. Stand. 11, 25 (1933).

1931 (1)

L. W. Tilton, J. Res. Nat. Bur. Stand. 6, 59 (1931).

1929 (1)

L. W. Tilton, J. Res. Nat. Bur. Stand. 2, 909 (1929).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 176.

Ditchburn, R. W.

R. W. Ditchburn, Light (Interscience Publishers, Inc., New York, 1963), 2nd ed., p. 346.

Edlén, B.

B. Edlén, Metrologia 2, 71 (1966).
[CrossRef]

Faick, C. A.

C. A. Faick, B. Fonoroff, J. Res. Nat. Bur. Stand. 32, 67 (1944).
[CrossRef]

Fonoroff, B.

C. A. Faick, B. Fonoroff, J. Res. Nat. Bur. Stand. 32, 67 (1944).
[CrossRef]

Forrest, J. W.

H. W. Straat, J. W. Forrest, J. Opt. Soc. Amer. 29, 240 (1939).
[CrossRef]

Guest, P. G.

P. G. Guest, W. M. Simmons, J. Opt. Soc. Amer. 43, 319 (1953).
[CrossRef]

Hughes, J. V.

J. V. Hughes, J. Sci. Instrum. 18, 234 (1941).
[CrossRef]

Molby, F. A.

F. A. Molby, J. Opt. Soc. Amer. 39, 600 (1949).
[CrossRef]

Penndorf, R.

R. Penndorf, J. Opt. Soc. Amer. 47, 176 (1957).
[CrossRef]

Simmons, W. M.

P. G. Guest, W. M. Simmons, J. Opt. Soc. Amer. 43, 319 (1953).
[CrossRef]

Straat, H. W.

H. W. Straat, J. W. Forrest, J. Opt. Soc. Amer. 29, 240 (1939).
[CrossRef]

Tilton, L. W.

L. W. Tilton, J. Res. Nat. Bur. Stand. 30, 311 (1943).
[CrossRef]

L. W. Tilton, J. Opt. Soc. Amer. 32, 371 (1942).
[CrossRef]

L. W. Tilton, J. Res. Nat. Bur. Stand. 14, 393 (1935).
[CrossRef]

L. W. Tilton, J. Res. Nat. Bur. Stand. 13, 111 (1934).
[CrossRef]

L. W. Tilton, J. Res. Nat. Bur. Stand. 11, 25 (1933).

L. W. Tilton, J. Res. Nat. Bur. Stand. 6, 59 (1931).

L. W. Tilton, J. Res. Nat. Bur. Stand. 2, 909 (1929).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 176.

Young, T. R.

T. R. Young, “Achromatic Interferometer for Gage Block Comparison,” Metrology of Gage Blocks, NBS Circular #581 (1957), p. 49.

J. Opt. Soc. Amer. (5)

R. Penndorf, J. Opt. Soc. Amer. 47, 176 (1957).
[CrossRef]

F. A. Molby, J. Opt. Soc. Amer. 39, 600 (1949).
[CrossRef]

L. W. Tilton, J. Opt. Soc. Amer. 32, 371 (1942).
[CrossRef]

H. W. Straat, J. W. Forrest, J. Opt. Soc. Amer. 29, 240 (1939).
[CrossRef]

P. G. Guest, W. M. Simmons, J. Opt. Soc. Amer. 43, 319 (1953).
[CrossRef]

J. Res. Nat. Bur. Stand. (7)

L. W. Tilton, J. Res. Nat. Bur. Stand. 30, 311 (1943).
[CrossRef]

C. A. Faick, B. Fonoroff, J. Res. Nat. Bur. Stand. 32, 67 (1944).
[CrossRef]

L. W. Tilton, J. Res. Nat. Bur. Stand. 2, 909 (1929).

L. W. Tilton, J. Res. Nat. Bur. Stand. 6, 59 (1931).

L. W. Tilton, J. Res. Nat. Bur. Stand. 11, 25 (1933).

L. W. Tilton, J. Res. Nat. Bur. Stand. 13, 111 (1934).
[CrossRef]

L. W. Tilton, J. Res. Nat. Bur. Stand. 14, 393 (1935).
[CrossRef]

J. Sci. Instrum. (1)

J. V. Hughes, J. Sci. Instrum. 18, 234 (1941).
[CrossRef]

Metrologia (1)

B. Edlén, Metrologia 2, 71 (1966).
[CrossRef]

Metrology of Gage Blocks (1)

T. R. Young, “Achromatic Interferometer for Gage Block Comparison,” Metrology of Gage Blocks, NBS Circular #581 (1957), p. 49.

Other (3)

Ref. 6, p. 267.

R. W. Ditchburn, Light (Interscience Publishers, Inc., New York, 1963), 2nd ed., p. 346.

M. Born, E. Wolf, Principles of Optics (Pergamon Press, Inc., New York, 1959), p. 176.

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Figures (3)

Fig. 1
Fig. 1

Errors in refractive index as listed in Table I for an 1 see of arc in angle measurement, plotted as a function of error the refracting angle and for various index values. Curves for Ka represent the situation where ΔA = +Δ(2D); curves for Kb represent the situation where ΔA = −Δ(2D). Values are to be multiplied by 10−6.

Fig. 2
Fig. 2

Permissible error in prism orientation for an index error of 1 × 10−6 as a function of refracting angle for various index values.

Fig. 3
Fig. 3

Ratio of the average refractive index error from inaccuracy of angle measurement in minimum deviation refractometry to the error from inaccuracy of angle measurement in autocollimating refractometry plotted as a function of the refractive index for various prism angles.

Tables (4)

Tables Icon

Table I Average Refractive Index Errors (Δnλ)av for 0.2 sec of arc Error in Angle Measurement in Minimum Deviation Refractometrya

Tables Icon

Table II Computed Refractive Index Errorsa in Minimum Deviation Refractometry for a Random Selection of Optical Glasses for Two Values of the Refracting Angle

Tables Icon

Table III Refractive Index of Air at Temperature of 22.0°C and Pressure of 760 torr Based on Penndorf’s Data

Tables Icon

Table IV The Four Elements of the Refractive Index Errora, for an Assumed Set of Measurement Uncertainties for Several Situations in V Block Refractometry

Equations (40)

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n λ = sin ( A + D λ ) / 2 sin ( A / 2 ) ,
Δ n λ = - sin ( D / 2 ) 2 sin 2 ( A / 2 ) Δ A + cos ( A + D ) / 2 4 sin ( A / 2 ) Δ ( 2 D ) ,
Δ A = Δ ( 2 D ) = Δ θ .
Δ n λ = - K Δ θ ,
Δ A = Δ ( 2 D ) = Δ θ , K a = 2 n cos ( A / 2 ) - 3 [ 1 - n 2 sin 2 ( A / 2 ) ] 1 2 4 sin ( A / 2 ) ,
Δ A = - Δ ( 2 D ) ; Δ A = Δ θ , K b = 2 n cos ( A / 2 ) - [ 1 - n 2 sin 2 ( A / 2 ) ] 1 2 4 sin ( A / 2 ) .
D = i 1 + i 2 - A = φ ( i 1 ) ,
Δ D = φ ( i 1 + Δ i 1 ) - φ ( i 1 ) ,
d 2 i 2 d i 1 2 = d 2 D d i 1 2 = 2 tan i 1 [ 1 - tan 2 ( a / 2 ) tan 2 i 1 ] ,
Δ D = tan i 1 [ 1 - tan 2 ( A / 2 ) tan 2 i 1 ] ( Δ i 1 ) 2 .
Δ i 1 = 4.862 ( k ) 1 2 [ n / ( n 2 - 1 ) ] 1 2 cos ( A / 2 ) ,
Δ n = - f ( 5.722 - 0.0457 / λ 2 ) × 10 - 8 ,
( n - 1 ) T P = ( n - 1 ) S ψ ( T , P ) ,
n T P = 1 + ( n 0 - 1 ) 1 + 0.003671 T 0 1 + 0.003671 T P P 0 ,
Δ ( n - 1 ) T P / ( n - 1 ) T P = Δ P / 760 - Δ T / 294.
n T = A + B ( T - τ ) 2 ,
Δ n = n T - n T + Δ T = [ - Δ T + Δ T 2 / ( T - τ ) ] ( d n / d T ) ,
n g 0 = [ sin ( A + D ) / 2 sin ( A / 2 ) ] T P [ 1 + ( n a o - 1 ) Q 0 P 1 + 0.003671 T ] - ( T - T 0 ) ( d n g / d T )
Q 0 = ( 1 + 0.003671 T 0 ) / P 0 .
n λ = sin i λ sin ( A / 2 ) ,
Δ n λ = - n λ cos ( A / 2 ) sin ( A / 2 ) Δ ( A / 2 ) + cos i λ sin ( A / 2 ) Δ i ,
Δ n λ = - K Δ θ ,
Δ ( A / 2 ) = Δ i = Δ θ , K a = n cos ( A / 2 ) - [ 1 - n 2 sin 2 ( a / 2 ) ] 1 2 sin ( A / 2 ) ,
Δ ( A / 2 ) = - Δ i ; Δ ( A / 2 ) = Δ θ , K b = n cos ( A / 2 ) + [ 1 - n 2 sin 2 ( A / 2 ) ] 1 2 sin ( A / 2 ) .
( K M D ) A V ( K A C ) A V = - 1 4 { 1 - n cos ( A / 2 ) [ 1 - n 2 sin 2 ( A / 2 ) ] 1 2 } .
n 2 2 cos 2 δ = n 1 2 + sin θ ( n 1 2 - sin 2 θ ) 1 2 + n 3 2 sin δ - ( n 1 / 2 ) sin 2 δ [ sin θ + ( n 1 2 - sin 2 θ ) 1 2 ] + 1 2 sin 2 δ [ sin θ + ( n 1 2 - sin 2 θ ) 1 2 - n 1 tan δ ] × [ 2 n 3 2 - n 1 2 - 2 sin θ ( n 1 2 - sin 2 θ ) 1 2 ] 1 2 ,
n 2 2 = n 1 2 + n 1 θ - n 1 2 δ + n 1 δ ( 2 n 3 2 - n 1 2 - 2 n 1 θ ) 1 2 .
2 n 2 ( Δ n 2 ) = ( 2 n 1 + θ ) Δ n 1 + n 1 Δ θ - n 1 [ n 1 - ( n 1 2 - 2 n 1 θ ) 1 2 ] Δ δ - { [ 2 n 1 + 2 n 1 θ / ( n 1 2 - 2 n 1 θ ) 1 2 ] Δ n 1 + [ n 1 2 / ( n 1 2 - 2 n 1 θ ) 1 2 ] ( Δ θ - 2 Δ n 3 ) } δ .
n i 0 + ( d n i / d T ) ( T i - T 0 ) = N 0 + ( d N / d T ) ( T i - T 0 ) ,
d n 10 / d T = d n 20 / d T = d n x 0 / d T = d n / d T ,
n x 0 = n 10 - ( n 10 - n 20 ) ( T x - T 1 ) / ( T 2 - T 1 ) .
Δ n x 0 = [ 1 - ( T x - T 1 ) / ( T 2 - T 1 ) ] Δ n 10 + [ ( T x - T 1 ) / ( T 2 - T 1 ) ] Δ n 20 - [ ( n 10 - n 20 ) / ( T 2 - T 1 ) 2 ] × [ ( T x - T 2 ) Δ T 1 - ( T x - T 1 ) Δ T 2 - ( T 2 - T 1 ) Δ T x ] .
( Δ n x 0 ) av = Δ n
( Δ n x 0 ) av = [ 1 - 2 ( T x - T 1 ) / ( T 2 - T 1 ) ] Δ n .
- [ ( n 10 - n 20 ) / 2 ( T 2 - T 1 ) ] [ - a 1 - a 2 + 2 a x ] Δ T ,
n 2 = sin A ( n 1 2 - n 3 2 sin 2 θ ) 1 2 + n 3 cos A sin θ ,
Δ n 2 = n 1 sin A ( n 1 2 - sin 2 θ ) 1 2 Δ n 1 + [ cos A ( n 1 2 - sin 2 θ ) 1 2 - sin A sin θ ] Δ A - [ sin A sin 2 θ 2 ( n 1 2 - sin 2 θ ) 1 2 - cos A cos θ ] Δ θ .
m = [ ( t 1 - t 2 ) / λ 0 ] ( n g - n a ) ,
n g = n a + m λ 0 / ( t 1 - t 2 ) .
Δ n g = Δ n a + [ ( n g - n a ) / t 1 - t 2 ) ] [ λ g Δ m - Δ ( t 1 - t 2 ) ] .

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