Abstract

The test of a mirror by the Ronchi method has shown to be very useful for testing concave aspherical mirrors. The analysis of a Ronchi pattern in order to find the experimental deviations of a given mirror whose theoretical shape is known, and the accuracy that can be obtained are described here.

© 1970 Optical Society of America

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References

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  1. A. Offner, Appl. Opt. 2, 153 (1963).
    [CrossRef]
  2. D. Malacara, Appl. Opt. 4, 1371 (1965).
    [CrossRef]
  3. M. V. R. K. Murty, J. Opt. Soc. Amer. 52, 768 (1962).
    [CrossRef]
  4. M. Born, E. Wolf. Principles of Optics (Pergamon Press, New York, 1959), p. 206.
  5. D. Malacara, Bol. Obs. Tonantzintla Tacubaya 47, 73 (1965).

1965 (2)

D. Malacara, Appl. Opt. 4, 1371 (1965).
[CrossRef]

D. Malacara, Bol. Obs. Tonantzintla Tacubaya 47, 73 (1965).

1963 (1)

1962 (1)

M. V. R. K. Murty, J. Opt. Soc. Amer. 52, 768 (1962).
[CrossRef]

Born, M.

M. Born, E. Wolf. Principles of Optics (Pergamon Press, New York, 1959), p. 206.

Malacara, D.

D. Malacara, Appl. Opt. 4, 1371 (1965).
[CrossRef]

D. Malacara, Bol. Obs. Tonantzintla Tacubaya 47, 73 (1965).

Murty, M. V. R. K.

M. V. R. K. Murty, J. Opt. Soc. Amer. 52, 768 (1962).
[CrossRef]

Offner, A.

Wolf, E.

M. Born, E. Wolf. Principles of Optics (Pergamon Press, New York, 1959), p. 206.

Appl. Opt. (2)

Bol. Obs. Tonantzintla Tacubaya (1)

D. Malacara, Bol. Obs. Tonantzintla Tacubaya 47, 73 (1965).

J. Opt. Soc. Amer. (1)

M. V. R. K. Murty, J. Opt. Soc. Amer. 52, 768 (1962).
[CrossRef]

Other (1)

M. Born, E. Wolf. Principles of Optics (Pergamon Press, New York, 1959), p. 206.

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Figures (7)

Fig. 1
Fig. 1

Ronchigram for Ritchey-Chrêtien primary mirror.

Fig. 2
Fig. 2

Geometrical interpretation of Ronchi fringes.

Fig. 3
Fig. 3

Sheared images of the optical surface due to diffraction on the Ronchi ruling.

Fig. 4
Fig. 4

Allowed values of the period in the ruling for different values of l.

Fig. 5
Fig. 5

Minimum permitted value of the period in the ruling.

Fig. 6
Fig. 6

Computing of TA (s) from ronchigram.

Fig. 7
Fig. 7

Theoretical and experimental aberrations compared.

Equations (33)

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Δ x = R · p / ( R l ) ,
W 1 = x 2 / 2 R ,
W 2 = ( x s ) 2 / 2 R .
OPD = W 1 W 2 = x s / R .
m λ = p sin θ ,
sin θ = s / ( R l ) ,
OPD = λ ( R l ) x / ( R · p ) .
Δ x = R p / ( R l ) .
d = θ l ,
d = λ l / p .
l λ / p R max p / 4 ( R max l ) ,
p 2 [ λ · l · R max l / ( R max ) ] 1 2 ,
Δ x max = R min p / ( R min l ) .
Δ x max 1 5 D ,
R min p / ( R min l ) 1 5 D ,
p D ( R min l ) / 5 R min .
R min l = 5 p R min / D ,
[ 1 + ( 100 λ R min 2 ) D 2 R max ] p 2 + ( 1 2 R min R max ) ( 20 λ R min ) D p 4 λ R min R max ( R max R min ) = 0.
( 1 + 100 λ R D 2 ) p 2 ( 20 λ R ) D p 4 λ Δ R = 0 .
p 2 20 λ ( R / D ) p 4 λ Δ R = 0 ,
p = 10 λ ( R D ) { 1 + [ 1 + Δ R 25 λ ( R / D ) 2 ] 1 2 }
Δ OPD ( ρ ) = 1 R [ 0 ρ Δ TA ( ρ ) d ρ ] ,
α TA ( ρ ) = x / ρ ,
TA ( ρ ) = α ρ / x .
TA ( ρ ) = α ( ρ ) ,
TA ( ρ ) = n p .
σ = δ ( Δ x ) / δ R ,
σ = p l / ( R l ) 2 .
σ = ( Δ x / R ) [ ( 1 Δ x ) / p ] .
δ TA min = p Δ x min / 10 Δ x .
Δ x min = 4 d = 4 λ l / p .
δ TA min = 2 5 ( λ l / Δ x ) .
δ TA min = 2 5 · λ l Δ x · R l = 2 5 λ R Δ x .

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