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BOLETÍN DE LOS OBSERVATORIOS DE TONANTZINTLA Y TACUBAYA, VOL. 4, Nœ27, 1965.

RONCHI

TEST

A N D TRANSVERSAL ABERRATION
])(11/iel 1\1a lacara

SPHERICAL

SI':\L-\RIO
La prucha dc Ronchi cs sumameute Útil para dctcrminar la (:alidad de sistemas ópticos que tendrían ahcrra<:Íón dc esfericidad transvcrsal. aÚu eu el caso de cstar perfectamente construidos. El propósito de este artículo es el de descrihir un método para calcular el ronchigrama; se supone que se puede calcular la aherraciÓu trans"ersal para cin, co rayos diferentes. que partau de un mismo punto luminoso sohre el ejc óptico.

Introdllctio/l

¿ Copyright 1965: Observatorio Astronómico Nacional, Universidad Nacional Autónoma de México

There is a very intimate relation between the transversal spherical aberration a 11([ the Ronchi~ram that is produced by means of a Ronchi ru[in~, It is of course assumed that the rulin~ has a low frequency, so that the ~eometrieal interpretation of the Ronchi pattern can be used. The Ronehi test is nearly a[ways limited to systems whieh, if perfeet, would produce straight (Ronchi ] 964) frin~es a 11([ any deviation from straightness would mean the presence of aberrations. fringes Exeeptions to this rule are the cases of some con cave mirrors. For instance, has been computed for parabolic surfaces tested at the center of curvature aberration. lhe ronchigram of any system with spherieal aberrathe shape 01' the (Sherwood ] 959) (Malacara ]965) but not for any reflecting 01' refractin~ sys-

a 11([a]so for general aspherical surfaces
tem having spherica]

The purpose of this papel' is lo ca1cu]ate tion, when tested on axis.

y

(X,y)

RONCHI RULING

x
I I I ,J I

~
oc.

ENTRANCE PUPIL
Figure l.-El/trance Pupil and ROl/chi Ruling Vit'wed along Ihe 0JJtical Axis.

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Fil/dil/g

of the RO/lchigram

The ronchigram of a system hadng spherical abcrration can be calculated assuming that the transversal aberration T A is a function 01' the distance S, between the ra)' amI the optical axis, over the entrance pupil. A view along the optical axis 01' an optical system amI a Ronchi ruling is represented in Fig. 1, where a is the distance between the central line on the ruling, amI the line that intercepts the ray coming fram a dark fringe. The quantities x, y amI O, shown
COS

in Fig. 1, are defined

as follows:

O

---- a TA (S)

x S (1)

thus
¿ Copyright 1965: Observatorio Astronómico Nacional, Universidad Nacional Autónoma de México

x
also:

aS TA (S)
(2)

(3) H D is the separation between two lines on the Ronchi a
__ 11

ruling,

a is given

by:

D,

(4)

where 1/ is an integer. A fringe on the ronchigram could be found by calculating many points (x, y) inside the entrance pupil for a constanl value of a, assuming that T A (S) is known for any value of S. Ir R is the radius o[ the en trance pupil, the following inequalily musl be satisfied: (5) Thus, in order to find the Ronchi fringe for a given value ol 1/, X amI )' al'c computed by giving S many values which lie between zero a 11<1 After giving a value to S ami calculating R. x by means of equation (2), it might happen that x > S: this wouhl mean that lhere is no fringe crossing the circle wilh radius S. To find the whole ronchigram, 11 is increased I'rom zero lO a value sllch that: (6) wherc T A""" is the maximum value 01' the transversal spherical aberralion for rays inside of the entrance pupil. The values 01' 1/ that satisfy this condition give all the Ronchi fringes [01' the oPlical system. CnlclIlatiol/ The transversal spherical of the ninth ordcr as follows: aberralion of T A (S) ver y accurately by a polynomial

on axis can be represented

T A (S)

=

nI S

+

a:1 S:\

+

n;? S.-,

+

n7 S7

+

al)

S!)

(7)
T A (S) for value is taken

Thus, the coefficients n, can be found by means 01' a matrix I'ive differenl value of S, using any ray tracing procedure. When as T Am(lz. T A (S) is calculated

inversion

after compuling the highest

for all desired points inside lhe aperlure,

Since the term ni S represents the defocusing lerm, the ronchigrams 01' lhe Ronchi ruling can be obtained with only one ray tracing, changing All the necessary ca1culations

for several different settings only the coefficient ni' computer.

can be made very easily wiLh the aid of an electronic

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A/Jplicalio/ls This method examples are given a) A Schmidt te, as shown in Fig.

of lhe MetllOd

of using the Ronchi test is ver)' uscful when riguring some optical systems: some below. plate corrector can be tested against the spherical mirror to be used with this pla2.

EXTENDED

I
¿ Copyright 1965: Observatorio Astronómico Nacional, Universidad Nacional Autónoma de México

SOURCE

~

~ '\

RONCHI RULING
-

t

t

PLATE tCORRECTING SPHERICAL MI RROR
]'igure 2.-Tt'slillg o/ II Schmidt Correctillg Plale.

b) The testing of a large refractor objcctive 1'01' an astronomical telescape generally requires a flat surface as big as the objective, 01' a collimatell beam 01' li!!;ht with the same apenurc. The objective can be Ronchi tested with a source at a rinite distance, by computing its trans,'ersal aberration. This is shown in Fig. 3.

,
POINT SO URCE

t
TELESCOPE O B J E CT I V E
Figure 3.-Testillg o/ 1I ?.arge Te/esco/,e Objectil'e

RONCHI RULlNG

t

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limated

Many olher lypes 01' systems could beam 01' light.

be lested in the same way, without
REFERENCES

having

to use a col-

l\falacara. n. Appl. Opt. 4, I:li I (HUi:;). ROllchi. V. Appl. Opt. 3, Hi (196-1). Shcrwood. A. A. J. I)roe. Roy. SoCo Ncw Walcs 43. 19 (1959).

¿ Copyright 1965: Observatorio Astronómico Nacional, Universidad Nacional Autónoma de México

lo

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