Abstract

Basic criteria are given for the design and use of a diffusion cell for a Rayleigh interferometer for membrane-transport studies. The effect of wave-front deflection on the fringe pattern is presented, as well as a numerical technique that allows the data to be corrected for deflection effects. A completely new type of diffusion cell is discussed that allows transport through membranes to be observed.

© 1975 Optical Society of America

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References

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  1. Louis J. Gosting and Lars Onsager, J. Am. Chem. Soc. 74, 6066 (1952).
    [Crossref]
  2. Gerson Kegeles and Louis J. Gosting, J. Am. Chem. Soc. 69, 2516 (1947).
    [Crossref] [PubMed]
  3. P. H. Bollenbeck and W. F. Ramirez, Biomedical Sci. Instrum. 7, 223 (1970).
  4. H. Svensson, Acta. Chem. Scand. 5, 72 (1951).
    [Crossref]
  5. Lewis G. Longworth, J. Am. Chem. Soc. 74, 4155 (1952).
    [Crossref]
  6. Louis J. Gosting, Adv. Protein Chem. 11, 429 (1956).
    [Crossref]
  7. M. Françon, Optical Interferometry, (Academic, New York, 1966), p. 7.
  8. P. H. Bollenbeck, Ph. D. thesis (University of Colorado, 1972).
  9. K. W. Beach, R. H. Muller, and C. W. Tobias, J. Opt. Soc. Am. 63, 559 (1973).
    [Crossref]
  10. P. H. Bollenbeck and W. F. Ramirez, I & EC Fund. 13, No. 4, 385 (1974).
    [Crossref]

1974 (1)

P. H. Bollenbeck and W. F. Ramirez, I & EC Fund. 13, No. 4, 385 (1974).
[Crossref]

1973 (1)

1970 (1)

P. H. Bollenbeck and W. F. Ramirez, Biomedical Sci. Instrum. 7, 223 (1970).

1956 (1)

Louis J. Gosting, Adv. Protein Chem. 11, 429 (1956).
[Crossref]

1952 (2)

Lewis G. Longworth, J. Am. Chem. Soc. 74, 4155 (1952).
[Crossref]

Louis J. Gosting and Lars Onsager, J. Am. Chem. Soc. 74, 6066 (1952).
[Crossref]

1951 (1)

H. Svensson, Acta. Chem. Scand. 5, 72 (1951).
[Crossref]

1947 (1)

Gerson Kegeles and Louis J. Gosting, J. Am. Chem. Soc. 69, 2516 (1947).
[Crossref] [PubMed]

Beach, K. W.

Bollenbeck, P. H.

P. H. Bollenbeck and W. F. Ramirez, I & EC Fund. 13, No. 4, 385 (1974).
[Crossref]

P. H. Bollenbeck and W. F. Ramirez, Biomedical Sci. Instrum. 7, 223 (1970).

P. H. Bollenbeck, Ph. D. thesis (University of Colorado, 1972).

Françon, M.

M. Françon, Optical Interferometry, (Academic, New York, 1966), p. 7.

Gosting, Louis J.

Louis J. Gosting, Adv. Protein Chem. 11, 429 (1956).
[Crossref]

Louis J. Gosting and Lars Onsager, J. Am. Chem. Soc. 74, 6066 (1952).
[Crossref]

Gerson Kegeles and Louis J. Gosting, J. Am. Chem. Soc. 69, 2516 (1947).
[Crossref] [PubMed]

Kegeles, Gerson

Gerson Kegeles and Louis J. Gosting, J. Am. Chem. Soc. 69, 2516 (1947).
[Crossref] [PubMed]

Longworth, Lewis G.

Lewis G. Longworth, J. Am. Chem. Soc. 74, 4155 (1952).
[Crossref]

Muller, R. H.

Onsager, Lars

Louis J. Gosting and Lars Onsager, J. Am. Chem. Soc. 74, 6066 (1952).
[Crossref]

Ramirez, W. F.

P. H. Bollenbeck and W. F. Ramirez, I & EC Fund. 13, No. 4, 385 (1974).
[Crossref]

P. H. Bollenbeck and W. F. Ramirez, Biomedical Sci. Instrum. 7, 223 (1970).

Svensson, H.

H. Svensson, Acta. Chem. Scand. 5, 72 (1951).
[Crossref]

Tobias, C. W.

Acta. Chem. Scand. (1)

H. Svensson, Acta. Chem. Scand. 5, 72 (1951).
[Crossref]

Adv. Protein Chem. (1)

Louis J. Gosting, Adv. Protein Chem. 11, 429 (1956).
[Crossref]

Biomedical Sci. Instrum. (1)

P. H. Bollenbeck and W. F. Ramirez, Biomedical Sci. Instrum. 7, 223 (1970).

I & EC Fund. (1)

P. H. Bollenbeck and W. F. Ramirez, I & EC Fund. 13, No. 4, 385 (1974).
[Crossref]

J. Am. Chem. Soc. (3)

Lewis G. Longworth, J. Am. Chem. Soc. 74, 4155 (1952).
[Crossref]

Louis J. Gosting and Lars Onsager, J. Am. Chem. Soc. 74, 6066 (1952).
[Crossref]

Gerson Kegeles and Louis J. Gosting, J. Am. Chem. Soc. 69, 2516 (1947).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

Other (2)

M. Françon, Optical Interferometry, (Academic, New York, 1966), p. 7.

P. H. Bollenbeck, Ph. D. thesis (University of Colorado, 1972).

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Figures (6)

FIG. 1
FIG. 1

Schematic representation of a modified Rayleigh interferometer for diffusion studies (top view).

FIG. 2
FIG. 2

Distortion of a collimated wave front by a refractive-index gradient.

FIG. 3
FIG. 3

Side view of test cell, showing bending of light rays by the refractive-index gradient.

FIG. 4
FIG. 4

Cell nomenclature for bending-correction calculations.

FIG. 5
FIG. 5

Glass diffusion cell.

FIG. 6
FIG. 6

Diffusion-cell cage and masking-slit assembly.

Tables (3)

Tables Icon

TABLE I Results of computer simulation to verify existence of a single plane of focus for refocusing deflected rays.

Tables Icon

TABLE II Results of computer simulation to show errors of the refractive-index gradient to be expected for the properly focused system when the bending effect is ignored.

Tables Icon

TABLE III Computer-simulation results, demonstrating convergence of iterative scheme for bending corrections.

Equations (41)

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I p = I 1 + I 2 p + 2 ( I 1 p I 2 p ) 1 / 2 | γ 12 ( θ ) | × cos ( α 12 ( 0 ) + 2 π λ 0 ( L 2 L 1 ) ) ,
( L 2 L 1 ) air = y s n a y F P / f ,
( L 2 L 1 ) cells = ( n 2 n 1 ) l .
I = ( sin ( 2 π a y F P / f λ 0 ) ( 2 π a y F P / f λ 0 ) ) 2 I 0 .
I p = 2 I 0 ( sin ( 2 π a y F P / f λ 0 ) ( 2 π a y F P / f λ 0 ) ) 2 × { 1 + | γ 12 ( θ ) | cos [ α 12 ( 0 ) + 2 π λ 0 ( ( n 2 n 1 ) l y s n a y F P f ) ] } .
d x d z = 1 n 0 0 s d n d x d s ,
Δ n = λ 0 / l ,
L sol = 0 s n ( x ) d s .
{ F i , x i } ,
{ F i , x 0 i } ,
( L D , i + 1 L R , i + 1 ) ( L D , i L R , i ) = ± λ 0 ,
( L D , i L R , i ) ( L D , 0 L R , 0 ) = ± F i λ 0 .
L D , i = ± F i λ 0 + ( L D , 0 L R , 0 ) + L R , i .
{ L D , i , x i 0 } .
L D = L 01 + L 12 + L 2 F P .
n ¯ = 0 S n ( x ) d x S .
L 01 = n ¯ S .
n ( x ) = n ( x 0 ) + [ d n d x ] 0 ( x x 0 ) .
n ¯ = n ( x 0 ) + 1 2 [ d n d x ] 0 ( x 1 x 0 ) .
n ( x 0 ) = n ¯ 1 2 [ d n d x ] 0 ( x 1 x 0 ) .
d x d s 1 n ( x ) 0 S d n d x d s .
d x d s 1 n ( x ) [ d n d x ] 0 S .
( x 1 x 0 ) = 1 n [ d n d x ] 0 S 2 2 .
( x 1 x 0 ) = 1 2 n ¯ 3 [ d n d x ] 0 L 01 2 .
L 12 = n g ( z 2 z 1 ) cos [ arcsin ( n g n ( x 1 ) sin α ) ] .
n ¯ i = L D , i n g ( z 2 z 1 ) L 2 F P , i ( z 1 z 0 ) .
n ¯ ( x ) = f ( x 0 ) .
( x i x 0 ) i = 1 2 n ¯ i [ d n d x ] 0 , i ( z 1 z 0 ) 2 .
n ( x 0 ) i = n ¯ i 1 2 [ d n d x ] 0 , i ( x 1 x 0 ) i .
s i 2 = ( x i x 0 ) i 2 + ( z 1 z 0 ) 2 .
sin α i = 1 n ¯ i [ d n d x ] 0 , i S i .
n ( x 1 ) i n ( x 0 ) i + [ d n d x ] 0 , i ( x 1 x 0 ) i .
sin β i = n ( x 1 ) i n g sin α i .
x 2 , i = x 1 , i + ( z 2 z 1 ) tan ( arcsin β i ) .
sin γ i = n g n a sin β i .
n i = L D , i L 12 , i L 2 F P , i s i
( x 1 x 0 ) i = 1 2 n ¯ i [ d n d x ] 0 , i S i 2 ;
n ( x 0 ) i = n ¯ i 1 2 [ d n d x ] 0 , i ( x 1 x 0 ) i ;
n ( x 0 ) = f ( x 0 ) ;
[ d n d x ] 0 = d d x f ( x 0 ) .
F i = N l λ 0 .