Misalignment study for a Dove prism for its
interferometric applications
Enoch Gutierrez, Marija Strojnik, and Gonzalo Paez
Centro de Investigaciones en Optica
Apdo. Postal 1-948, C.P. 37000, Leon, Guanajuato, Mexico
enoch@cio.mx
Abstract
It is our interest to design, fabricate and characterize a Dove prism for interferometric use. In a
previous work, we determined the prism tolerance to manufacturing errors and evaluate the change in
the image quality introduced by this performance deterioration. In the present work, we determine the
tolerance to misalignment of the Dove prism for its incorporation into a Rotationally-Shearing
Interferometer (RSI). We show that it is possible to reduce the wave-front deviation caused by base
angle errors with a specific optical misalignment. The misalignment analysis of a Dove prism with a
1.515 refraction index shows that to ensure a maximum OPD of /10 (at 633 nm) the tolerance to
misalignment has to be ± 0.33 arc sec.
Keywords: Dove prism, Misalignment, Exact ray trace
1. Introduction
Dove prisms have found wide use in traditional optical systems as image erectors. Recently, the
implementation of prisms in interferometers has been on the rise.1-3
In our group, we have proposed a Dove prism as the main optical element of a Rotationally-Shearing
Interferometer (RSI). The RSI is built on the basis of a traditional Mach-Zehnder interferometer with
the addition of a rotational system (a Dove prism) on one arm, with the purpose of shearing (rotating)
the wave front.4,5 The RSI sensitivity may be increased by decreasing the shearing angle.6,7 This
interferometer has been suggested for distinct applications.8,9
The manufacturing quality of the Dove prisms and a suitable alignment determine the performance of
RSI.10 Formerly, other groups have analyzed alignment problems and the quality of manufacture in
rotational prisms for conventional imaging systems.11,12 However, interferometric implementation of a
Dove prism restricts the manufacturing errors and the misalignment that can be tolerated. For this
reason, we have determined suitable parameters and tolerance to manufacturing errors.13,14
2. Misalignment analysis of a Dove prism
In this work, we determine the tolerance to misalignment of a Dove prism within a RSI. In order to
measure a /5 tilt into the RSI, in accordance with Nyquist theorem, a maximum wave-front deviation
of /10 (at 633 nm) is assumed as acceptable.
Our analysis considers that the Mach-Zehnder interferometer is perfectly aligned. Therefore, the
obtained OPD at the observation plane is only due to manufacturing errors and misalignment of the
Dove prism.
The exact ray trace program used in this analysis
was previously developed by our infrared group.14
Xi

Now, we introduce an Euler transformation matrix
x
x’
and several programming routines in order to study
the lack of accuracy in the alignment of the Dove
Xo
y’
Yi

y
Yo
prism. This matrix helps to model the x-axis and yaxis rotations of the prism. It is important to keep
in mind that in this analysis we consider plane
surfaces within an afocal system.
Fig. 1. Misalignment sketch of a Dove prism.
The parameters of the analyzed Dove prism are:
length = 107.56 mm, height = 25.4 mm (square aperture), base angle = 45° and refraction index =
1.515. Prism misalignment is indicated by means of the coordinate system rotation (Δα, Δ) of the
prism (see Figure 1). The obtained data are taking into account an analyzed area of 60% for each
surface. Along this work, we use the symbolism and the sign conventions used in Ref. 14, with
exception of the base angle error to avoid a possible confusion with the coordinate system rotation in
the y-axis.
We study the worst case for the pyramidal angle (1 + 2) and the base angle error () separately.
This helps us to identify the consequences of a misalignment on the image affected by each
manufacturing error. The worst case for each error is fulfilled when: -1 = 2 and 1 = 2.14
First, we discuss the OPD caused by the prism misalignment for three different magnitudes of each
manufacturing error. Afterward, we determine the tolerance to misalignment of an interferometric
Dove prism.14
A Dove prism with 120 arc sec base angle error (the worst case) causes a slight OPD (smaller than
0.03) when it is rotated on the x-axis in an interval of 200 arc sec. Hence, this misalignment is
neglected for practical purposes in the first analysis.
Figure 2 illustrates the y-axis
rotation of the real Dove prism with
base angle errors of 120, 60 and
20 arc sec. This figure shows that
when no rotation is introduced, an
OPD also exists, due to the base
angle
Fig. 2. Decrease of the OPD brings about y-axis rotation of a
Dove prism. The base angle errors of the modeled prism, in
the worst case (-1 = 2), are: 120, 60 and 20 arc sec.
OPD, through y-axis rotation, has the same gradient in the
three cases. Therefore, the prism has the same tolerance to
misalignment no matter the magnitude of the base angle
error.
error.
However,
this
problem could be eliminated with a
suitable prism misalignment.
As we can see above, the OPD
due to any base angle error has an identical rate of change with respect to the prism rotation angle in
all cases. It is important to mention that the rate of change is dependent on the refraction index of the
prism. Hence, the prism always has the same tolerance to misalignment to ensure maximum OPD,
regardless of the magnitude of the base angle error.
On the other hand, figure 3 depicts the y-axis rotation of the real prism with pyramidal angles of 240,
120 and 40 arc sec. In contrast to the base angle error, the OPD given by the pyramidal angle could
not be eliminated by any prism rotation. Therefore, the ideal position of a prism with a pyramidal
angle is when it is perfectly aligned, unlike a prism with a base angle error.
Finally, we study the misalignment of
the
interferometric
Dove
prism
(tolerance to manufacturing error of ±
0.35 arc sec).
In this analysis we
neglect the study of the pyramidal
error
due
to
the
aforementioned
information. We start by rotating the
prism round the x-axis. Table 1 shows
Fig. 3. Increase of the OPD brings about y-axis rotation of a real
Dove prism. Pyramidal angle of the modeled prisms, in the
worst case (1 + 2), are: 240, 120 and 40 arc sec. OPD
caused by pyramidal angle could not be eliminated, on the
contrary it rises. Therefore, the ideal position of a prism with
pyramidal angle is the perfect alignment.
the maximum OPD obtained for this
rotation.
As we see in figure 5, the
interferometric prism rotation round
the x-axis does not modify the OPD
caused by the base angle error.
Table 1. The maximum OPD due to x-axis and y-axis rotations of an interferometric Dove prism.
x-axis rotation
y-axis rotation
α [arc sec]
OPD/
 [arc sec]
OPD/
- 1.42
0.09
- 1.42
0.52
2.05
0.09
2.05
0.52
We also rotate the interferometric prism
in the y-axis (see Figure 4).
The
maximum
this
OPDs
due
to
misalignment are shown in table 1. The
wave-front deviation is a consequence
of the inversion property of a Dove
prism and the base angle error.
Fig. 4. OPD due to x-axis and y-axis rotations of an
interferometric Dove prism. We analyze the worst case
in the base angle error (1 = -2). To ensure a
maximum OPD of /10 due to interferometric Dove
prism misalignment, the tolerance to misalignment is of
± 0.33 arc sec.
The
misalignment
analysis
of
the
interferometric Dove prism shows that
to ensure a maximum OPD of /10 (at 633 nm), the tolerance to misalignment is of ± 0.33 arc sec.
This tolerance to misalignment is the same for any Dove prism with a refraction index of 1.515 (BK7).
3. Summary
We analyzed the Dove prism misalignment for its incorporation into a RSI. This analysis showed that
the OPD given by the pyramidal angle could not be compensated with any prism misalignment, in
contrast to the base angle error. The only possibility to compensate this error is to misalign the
interferometer arm that contains the prism, in the y direction, until the OPD is removed.
We saw that the Dove prism always has the same tolerance to misalignment regardless of the
magnitude of the manufacturing error. The analysis of the interferometric Dove prism showed that to
ensure a maximum OPD of /10 (at 633 nm), the tolerance to misalignment is of ± 0.33 arc sec. This
tolerance is for any Dove prism with a refraction index of 1.515.
References
1. C. Ramirez, M. Strojnik, and G. Paez, “Performance evaluation of a wave-front displacement system for
vectorial shearing interferometer,” Opt. Commun., submitted for publication.
2. D. A. Flickinger, R. N. Coffee, G. N. Gibson, and T. C. Weinacht, “Bichromatic, phase compensating
interferometer based on prism pair compressors,” Appl. Opt. 45(24), 6187-6191 (2006).
3. G. Garcia-Torales, G. Paez, and M. Strojnik, “Simulations and experimental results with a vectorial shearing
interferometer,” Opt. Eng. 40(5), 767-773 (2001).
4. M. S. Scholl, “Applicability of rotationally-shearing interferometer to the testing if the optical systems without
rotational symmetry,” in Infrared Spaceborne Remote Sensing IV, Proc. SPIE 2817, 187-197 (1996).
5. G. Paez, and M. Strojnik, “Differential Rotationally-shearing Interferometer: Implementation Concept,” in
Infrared Technology and Applications XXIII, Proc. SPIE 3061, 417-424 (1997).
6. G. Paez, and M. Strojnik, “Simulated interferometric patterns of a rotationally-shearing interferometer,” in
Infrared Spaceborne Remote Sensing V, Proc. SPIE 3122, 236-252 (1997).
7. M. Strojnik, and G. Paez, “Mathematical theory of differential rotational shearing interferometry: asymmetrical
aberrations,” in Interferometry '99: Techniques and Technologies, Proc. SPIE 3744, 335-346 (1999).
8. J. Flores, G. Paez, and M. Strojnik, “Optimal aperture configuration for a segmented and partially diluted
extremely large telescope,” J. Mod. Optic. 50(5), 729-742 (2003).
9. M. S. Scholl, “Infrared signal generated by a planet outside the solar system discriminated by a rotating
rotationally-shearing interferometer,” Inf. Phys. & Tech. 37(3), 307-312 (1996).
10. J. Sandoval, G. Paez, and M. Strojnik, “Opto-mechanical design of a prism rotator,” in Infrared Spaceborn
Remote Sensing IX, Proc. SPIE 4486, 170-180 (2001).
11. D. L. Sullivan, “Alignment of Rotational Prisms,” Appl. Opt. 11(9), 2028-2032 (1972).
12. J. B. Houston, and B. H. Walker, “Pechan derotation prism application & alignment notes”, Opt. Eng. 13(6),
G233-G234 (1974).
13. I. Moreno, G. Paez, and M. Strojnik, “Dove prism with increased throughput for implementation in a
rotational-shearing interferometer,” Appl. Opt. 42(22), 4514-4521 (2003).
14. E. Gutierrez, M. Strojnik, G. Paez, and P. Vacas-Jaques, “Interferometric tolerance determination for a Dove
prism using exact ray trace,” Opt. Commun., submitted for publication.