Abstract

A method for calculating the geometrical Ronchi pattern of any aspheric mirror with the point source at any point along the optical axis is described. If a mirror gives a Ronchi pattern that is different from the one calculated, the deviations of this mirror from its ideal shape can be found.

© 1965 Optical Society of America

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References

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  1. V. Ronchi, Appl. Opt. 3, 437 (1964).
    [Crossref]
  2. G. Toraldo di Francia, Optical Image Evaluation, Natl. Bur. Std. (U.S.), Circ. 526 (U.S. Govt. Printing Office, Washington, D.C., 1954), p. 161.
  3. V. A. Komissaruk, Opt. Spectry. 16, 571 (1964).
  4. I. Adachi, Atti Fond. G. Ronchi 15, 461 (1960).
  5. I. Adachi, Atti Fond. G. Ronchi 17, 252 (1962).
  6. A. A. Sherwood, J. Proc. Roy. Soc. New South Wales 43, 19 (1959).

1964 (2)

V. Ronchi, Appl. Opt. 3, 437 (1964).
[Crossref]

V. A. Komissaruk, Opt. Spectry. 16, 571 (1964).

1962 (1)

I. Adachi, Atti Fond. G. Ronchi 17, 252 (1962).

1960 (1)

I. Adachi, Atti Fond. G. Ronchi 15, 461 (1960).

1959 (1)

A. A. Sherwood, J. Proc. Roy. Soc. New South Wales 43, 19 (1959).

Adachi, I.

I. Adachi, Atti Fond. G. Ronchi 17, 252 (1962).

I. Adachi, Atti Fond. G. Ronchi 15, 461 (1960).

Komissaruk, V. A.

V. A. Komissaruk, Opt. Spectry. 16, 571 (1964).

Ronchi, V.

Sherwood, A. A.

A. A. Sherwood, J. Proc. Roy. Soc. New South Wales 43, 19 (1959).

Toraldo di Francia, G.

G. Toraldo di Francia, Optical Image Evaluation, Natl. Bur. Std. (U.S.), Circ. 526 (U.S. Govt. Printing Office, Washington, D.C., 1954), p. 161.

Appl. Opt. (1)

Atti Fond. G. Ronchi (2)

I. Adachi, Atti Fond. G. Ronchi 15, 461 (1960).

I. Adachi, Atti Fond. G. Ronchi 17, 252 (1962).

J. Proc. Roy. Soc. New South Wales (1)

A. A. Sherwood, J. Proc. Roy. Soc. New South Wales 43, 19 (1959).

Opt. Spectry. (1)

V. A. Komissaruk, Opt. Spectry. 16, 571 (1964).

Other (1)

G. Toraldo di Francia, Optical Image Evaluation, Natl. Bur. Std. (U.S.), Circ. 526 (U.S. Govt. Printing Office, Washington, D.C., 1954), p. 161.

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Figures (3)

Fig. 1
Fig. 1

Arrangement of elements for the Ronchi test.

Fig. 2
Fig. 2

Projection of Ronchi fringes over a plane.

Fig. 3
Fig. 3

Deviation of rays on a deformed mirror.

Equations (32)

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f ( x , y ) z = 0 .
N = [ f x i f y j + k ] [ 1 + ( f x ) 2 + ( f y ) 2 ] ½ .
S 1 = [ x i + y j ( L f ) k ] [ x 2 + y 2 + ( L f ) 2 ] ½ .
S 2 = S 1 2 ( S 1 · N ) N .
S 2 = ( S 2 ) i x + ( S 2 ) j y + ( S 2 ) k z .
( S 2 ) x ( S 2 ) z = x [ 1 ( f x ) 2 + ( f y ) 2 ] 2 f x [ y f y + ( L f ) ] ( f L ) [ ( f x ) 2 + ( f y ) 2 1 ] + 2 [ x f x + y f y ] .
R = ( x 2 + y 2 ) ½ .
( S 2 ) x ( S 2 ) z = x [ 1 ( d f d R ) 2 2 ( L f ) R d f d R ] ( L f ) [ 1 ( d f d R ) 2 ] + 2 R d f d R .
( α x ) ( S 2 ) x = ( y 0 y ) ( S 2 ) y = ( D f ) ( S 2 ) z ,
α x D f = ( S 2 ) x ( S 2 ) z .
x α = ( L f ) [ 1 ( d f d R ) 2 ] + 2 R d f d R ( D + L 2 f ) [ 1 ( d f d R ) 2 ] + 2 d f d R [ R ( D f ) ( L f ) R ] .
cos θ α = L f R [ 1 ( d f d R ) 2 ] + 2 d f d R ( D + L 2 f ) [ 1 ( d f d R ) 2 ] + 2 d f d R [ R ( D f ) ( L f ) R ] .
R R p f ( R ) f ( R ) = R α sec θ D f ( R ) .
R p = R [ 1 ( f ( R ) f ( R ) D f ( R ) ) ( 1 α R cos θ ) ] .
tan β = d f ( R ) d R .
tan ( β + δ β ) = d [ f ( R ) + δ f ( R ) ] d R .
δ tan β = tan ( β + δ β ) tan β = d [ δ f ( R ) ] d R .
( sec 2 β ) δ β = d [ δ f ( R ) ] d R .
g ( R ) = δ f ( R ) cos β .
δ β = cos β d g ( R ) d R .
δ γ = 2 cos β d g ( R ) d R .
tan γ = R b D f ( R ) .
d g ( R ) d R = ( cos 2 γ ) δ b 2 [ D f ( R ) ] cos β .
d g ( R ) d R = ( D f ) [ R 2 + ( r f ) 2 ] ½ δ α ( r f ) [ ( R b ) 2 + ( D f ) 2 ] cos θ .
d g ( R ) d R = δ α 2 D cos θ .
δ α ( R ) = b 2 R + b 4 R 3 + b 4 R 3 + b 6 R 5 + b 8 R 7 + b 10 R 9 .
g ( R ) = a 2 R 2 + a 4 R 4 + a 6 R 6 + a 8 R 8 + a 10 R 10 ,
a 2 = b 2 / 4 D cos θ ,
a 4 = b 4 / 8 D cos θ ,
a 6 = b 6 / 12 D cos θ ,
a 8 = b 8 / 16 D cos θ ,
α 10 = b 10 / 20 D cos θ .

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