COL 11(3), 032201(2013) CHINESE OPTICS LETTERS March 10, 2013
Design and fabrication of computer-generated
holograms for testing optical freeform surfaces
Hua Shen (
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)
1,2
, Rihong Zhu (
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FFF
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)
1∗
, Zhishan Gao (
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)
1
,
E. Y. B. PUN
2
, W. H. Wong
2
, and Xiaoli Zhu (
ÁÁÁ
ááá
)
3
1
School of Electronic Engineering and Photo-Electric Technology, Nanjing University of Science and Technology,
Nanjing 210094, China
2
Department of Electronic Engineering, City University of Hong Kong, Kowloon Tang, Hong Kong 999077, China
3
Key Laboratory of Nano-Fabrication and Novel Devices Integrated Technology,
Institute of Microelectronic of Chinese Academy of Sciences, Beijing 100029, China
∗
Corresponding author: zhurihong@mail.njust.edu.cn
Received October 23, 2012; accepted November 5, 2012; posted online February 6, 2013
Freeform optical surfaces (FOSs) will be the best elements in the design of compact optical systems in the
future. However, it is ex tremely difficult to measure freeform surface with sufficient accuracy, which im-
pedes the development of the freeform surface. The design and fabrication of computer-generated hologram
(CGH) , which has been successfully applied to the tests for aspheric surfaces, cannot be directly adopted
to test FOSs due to their non-rotational asymmetry. A novel ray tracing planning method combined with
successively optimizing even and odd power coefficients of phase polynomials in turn is proposed, which
can successfully design a non-rotational asymmetry CGH for the tests of FOSs with an F -θ lens. A new
eight-step fabrication process is also presented aiming to solve the problem that the linewidth on the same
circle of the CGH for testing freeform surface is not uniform. This problem cannot be solved in the original
procedure of CGH fabrication. The test results of the step profiler show that the CGH fabricated in the
new procedu re meets the requirements.
OCIS codes: 220.1250, 050.1970, 090.1760, 220.4840.
doi: 10.3788/COL201311.032201.
Original optical systems composed by spherical and as-
pheric surfaces cannot s atisfy the increasing demands for
compactness and high qua lity with the development of
the photo-electric technology. Freeform optical elements
are widely used in many optoelectronic systems because
they can correc t se veral image aberrations effectively and
simplify optical system structures
[1,2]
. It has attracted
considerable attention to design and fabricate several
freeform surfac e s
[3,4]
. But the fabrication costs are too
high and the q uality of the free form surfaces are not as
good as aspheric surfaces because it is extremely difficult
to accurately measure the quality of the freefo rm sur-
faces, which has been the focus in the o ptica l measure-
ment field
[5,6]
.
The interferometric method with computer generated
hologram (CGH) is successfully applied to the precise
testing of aspheric surfaces because CGH ca n provide
arbitrary shape wavefront that compensates the de-
parture of the tested surface from a spherica l one in
null test
[7−12]
. Using CGH as a null corrcetor in the
tests of freefor m surfaces is feasible a nd valid because
the freeform s urfaces can be regarded a s non-rotational
asymmetry aspheric surfaces
[13]
. However, when CGH
is adopted to test free fo rm surfa c es, the design, fabri-
cation and alignment of CGH have be e n facing techni-
cal barriers caused by free shape, rapid gradient change,
and definition difficulty of freeform sur fa c es. Until now,
there are few reports on fabrication of non-rotational
asymmetry CGH, and some of them focused on the de-
sign of non-rotationa l asymmetry CGH
[14,15]
using cubic
B-spline interpolatio n. A novel design method based on
orthogonal basis set and fabrication process of CGH used
in tests of freeform surface with an F -θ lens is presented
below.
When CGH is used for testing aspheric surfaces, ac-
cording to the aplanatic principle, all optical paths from
F
′
to the tested surface are equa l, as shown in Fig. 1
[14]
.
Supposing the ray going thr ough the p oint G
0
on the
surface is the reference ray and considering an arbitrary
ray launches onto G on the tested surface along the cor-
responding normal direction, the optical path difference
is
w(x
s
, y
s
, z
s
) = |F
′
E| + n
2
|ET | + |T G|
− |F F
′
| − n
2
|F R| − |RG
0
| , (1)
where n
2
is the refra c tive index of the substrate of the
CGH. |F
′
E|,|ET |,|T G|, |F F
′
|,|F R|, and |RG|
0
can be
calculated by ray tracing. The phase distribution of the
CGH is
φ(x
s
, y
s
, z
s
) = 2π · w(x
s
, y
s
, z
s
)/λ, (2)
where λ is the working wavelength.
Due to the rotational symmetry of the aspheric sur-
faces, the phase of each point on the same circle of CGH
can be obtained as long as that of one point is calculated
from Eqs. (1) and (2). Therefore, the phase function ca n
be described as
φ(ρ) =
N
X
i=1
α
i
ρ
2i
, (3)
where N is the number of polynomial c oefficients in
series, the coordinate ρ is the ra dius generalized by the
1671-7694/2013/032201(5) 032201-1
c
2013 Chinese Optics Letters
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