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First-order design of a reflective viewfinder for

adaptive optics ophthalmoscopy

Alfredo Dubra1,2,3,* and Yusufu N. Sulai4

1Department of Ophthalmology, Medical College of Wisconsin, Milwaukee, Wisconsin 53226, USA

2Department of Biophysics, Medical College of Wisconsin, Milwaukee, Wisconsin 53226, USA

3Department of Biomedical Engineering, Marquette University, Milwaukee, Wisconsin 53233, USA

4The Institute of Optics, University of Rochester, Rochester, New York 14627, USA

*adubra@mcw.edu

Abstract: Adaptive optics (AO) ophthalmoscopes with small fields of view

have limited clinical utility. We propose to address this problem in

reflective instruments by incorporating a viewfinder pupil relay designed by

considering pupil and image centering and conjugation. Diverting light

from an existing pupil optical relay to the viewfinder relay allows switching

field of view size. Design methods that meet all four centering and

conjugation conditions using either a single concave mirror or with two

concave mirrors forming an off-axis afocal telescope are presented. Two

different methods for calculating the focal length and orientation of the

concave mirrors in the afocal viewfinder relay are introduced. Finally, a 2.2

× viewfinder mode is demonstrated in an AO scanning light

ophthalmoscope.

©2012 Optical Society of America

OCIS codes: (080.4035) Mirror system design; (110.1080) Active or adaptive optics;

(170.3890) Medical optics instrumentation; (170.4460) Ophthalmic optics and devices.

References

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imaging,” Invest. Ophthalmol. Vis. Sci. 52(8), 5473–5480 (2011).

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imaging of the human rod photoreceptor mosaic using a confocal adaptive optics scanning ophthalmoscope,”

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Received 20 Aug 2012; revised 5 Oct 2012; accepted 5 Oct 2012; published 12 Nov 2012

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1. Introduction

Ophthalmic AO imaging allows visualization of the living retina at the microscopic scale by

compensating for the monochromatic aberrations of the optics of the eye. Thanks to advances

in optical design, wavefront correctors and light sources, the technology has matured to the

extent that microscopic structures can be routinely imaged with research AO

ophthalmoscopes [1–9] and commercial prototypes [10–12].

Most current reflective AO ophthalmoscopes can achieve only small fields of view

(FOVs) compared to non-AO ophthalmoscopes, making it difficult to navigate the retina. This

limitation in reflective instruments typically stems from either the small angles of incidence

(and hence mirrors) required to achieve good optical performance or the small Lagrange

invariant of fast resonant optical scanners. Current resonant scanners that can achieve larger

scanning angles at the eye resonate at audible frequencies (e.g. 8 KHz [13]). The loud high-

pitch sound of these scanners makes them undesirable. The lack of a viewfinder must be

addressed for ophthalmic AO imaging to achieve its full clinical potential.

AO ophthalmoscopes can be thought of as a series of optical elements that relay the exit

pupil of the eye onto a number of optical scanners, wavefront correctors, wavefront sensors,

apodizing masks, etc [14–16]. We propose diverting light from one of these pupil relays onto

an alternative relay that we will refer to as the viewfinder relay, with larger angular

magnification and a proportionally smaller pupil magnification. The larger FOV allows

searching for features of interest and accurately pinpointing the location of the smaller FOV.

Although the proposed viewfinder mode would in most cases not provide as large a FOV as

most clinical instruments (i.e. 15°), it would benefit from the AO correction of the

monochromatic aberrations of the eye.

Diversion of light to the viewfinder relay could be achieved in at least three different

ways: by moving the optical elements with optical power, by using a different wavelength

with fixed dichroics, or by using moveable fold mirrors. In the first approach, the light

throughput could remain unchanged if the number of optical elements used is kept constant. If

the elements with optical power in the original relay have to be moved in order to switch to

the viewfinder mode, their alignment, and hence the AO correction could be compromised.

Using different wavelengths with fixed dichroics to incorporate the viewfinder relay to the

optical setup would allow simultaneous viewing of the high- and low-magnification FOVs.

This approach has the advantage of no moving parts, but results in lower light throughput and

it requires an additional light source and detector. The third alternative, using moveable

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Received 20 Aug 2012; revised 5 Oct 2012; accepted 5 Oct 2012; published 12 Nov 2012

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folding mirrors might be the cheapest and simplest to implement, because the alignment of the

original relay is not affected and no additional light source(s) or detector(s) are required.

The rest of this work describes the first-order design of viewfinder relays using either one

or two concave mirrors, followed by the demonstration of an afocal viewfinder relay in an AO

scanning light ophthalmoscope (AOSLO).

2. Theory

There are four conditions relating pupil and image planes that should be considered in the

first-order design of a reflective viewfinder relay for an AO ophthalmoscope:

• Pupil plane centering. By definition, the exit pupil of the viewfinder relay is smaller

than that of the original relay. In order to avoid vignetting, the viewfinder relay exit

pupil needs to be contained within, but not necessarily centered with respect to the

exit pupil of the original relay.

• Image plane centering. By definition, the FOV of the viewfinder relay is larger than

that of the original relay, and the latter is usually centered with respect to the former.

• Pupil plane conjugation. In order to avoid degradation of the AO correction and/or

vignetting, the exit pupil plane of the viewfinder relay should be conjugate to that of

the original relay.

• Image plane conjugation. In order to maintain focus when switching to the viewfinder

mode, light exiting the viewfinder relay must have the same vergence as that exiting

the original relay.

In practice, a viewfinder relay can be implemented meeting only some of the four

conditions listed above and with an arbitrary number of optical elements. In what follows, we

will discuss how to design a viewfinder relay with either one or two concave mirrors.

2.1 Single concave mirror viewfinder relay

A single concave mirror can be chosen to simultaneously meet the pupil and image plane

conjugation conditions, as well as one of the centering conditions, but not both. Hence, at

least one additional fold mirror is required. The focal length of the concave mirror should be

chosen based on the desired relative angular magnification of the viewfinder

θ

0

MMM

where

0

M and

1

M are the pupil magnification for the original and viewfinder

relays, respectively. Image conjugation can be ensured by forcing the exit vergence of the

viewfinder relay to be the same as that of the original relay.

According to paraxial ray tracing the vergence at the exit pupil of the relay when using a

single concave mirror (see Fig. 1) is

f

P

1,

0

2

1

,

faPfa

f

(1)

where f is the focal length of the mirror, a is the separation between the entrance pupil and

the mirror, and

magnification and Eq. (1) we get

0P is the initial vergence. Using the lens equation, the definition of transverse

2

0f

1

.

M

a

P M P

(2)

which in terms of

θ

M becomes

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Received 20 Aug 2012; revised 5 Oct 2012; accepted 5 Oct 2012; published 12 Nov 2012

19 November 2012 / Vol. 20, No. 24 / OPTICS EXPRESS 26598

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θθ

0

2

θ2

00f

.

MMM

a

MP M P

(3)

Then, using the lens equation and the definition of magnification, it follows that

0

θ

0

,

aM

f

MM

(4)

with the separation of the mirror and the exit pupil plane of the relay being given by Eqs. (3)

and (4) and the lens equation. These formulae indicate that a viewfinder relay with a single

mirror can simultaneously meet the pupil and image plane conjugation conditions, when the

denominator of Eq. (3) is not zero. When the denominator is zero, the original relay can be

thought of as an afocal telescope, which is the case for most current reflective AO

ophthalmoscopes. Thus, in what follows, we will discuss a viewfinder relay assuming an

afocal original relay.

Fig. 1. Pupil relay formed by a single concave mirror with focal length f. The mirror is a

distance a from the entrance pupil, while the exit pupil is at a distance a f / (a - f). P0 and Pf are

the initial and final vergences of the imaging beam.

2.2 Reflective afocal viewfinder relay

The optical axis of the original relay can be described by the three vectors depicted in Fig. 2.

For simplicity and without loss of generality it can be assumed that in this telescope, the first

vector starts at the origin of coordinates and lies along the x-axis, while the second vector lies

on the x-y plane. If the focal lengths of the mirrors are f1 and f2 and the angles of incidence of

the optical axis onto the mirrors by I1xy, I2xy and I2z, (I1z = 0), then the three vectors in

Cartesian coordinates are

322z 2xy 1xy

cos 2 cos 22, cos 2

fIII

In the viewfinder telescope (primed variables) the reflection off the first mirror is not

necessarily contained within the x-y plane, and thus an additional angle (I’1z) is required to

define the vectors corresponding to the viewfinder telescope,

1

2121xy1xy

2z2xy1xy

I

2z

1,0,0 ,

cos 2,sin 2 ,0 ,

sin 22,sin 2.

f

ffII

III

1v

v

v

(5)

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1

' 1,0,0 ,

21

'

2 1xy1z 1xy1z1z

32 2z2xy 1xy 2z 2xy1xy2z

'

'' cos 2 ' cos 2 ',sin 2 'cos 2 ',sin 2 ',

''cos 2 'cos 2 '2 '

I

, cos 2 '

sin 2 ' 2 '

I

,sin 2 '.

f

ffIIIII

fIIIII

1

v

v

v

(6)

Fig. 2. Vectors used to describe the optical axis of an off-axis reflective afocal telescope

formed by two concave mirrors (M1 and M2), projected on the x-y plane.

Keeping the modulus of

conjugation to that of the original telescope. Forcing the modulus of

of the new mirrors’ focal lengths guarantees the same image conjugation as that of the

original telescope. These conditions, combined with imposing that the pupil and image planes

are centered can be summarized as,

1' v and

3' v as

1' f

and

2' f

respectively, maintains the exit pupil

2' v to be equal to the sum

11

'

'

'

'

33

22

123123

',

,

'' .

ff

v

f

v

f

11

vv

v

vvvvv

(7)

The six unknowns in these equations (f’1, f’2, I’1xy, I’1z, I’2xy and I’2z) determine the placement

and orientation of the viewfinder relay mirrors. With some rearrangement, these equations

translate into five independent equations, with the last three being summarized as a vector

equation,

2z

'

'

2z

2xy

'

1xy2xy 1xy

I

1

'

2

2123

12

,

,

'

'11.

I

I

I

II

ff

ff

vvvv

(8)

Because there are only five equations and six variables, one degree of freedom remains,

which can be conveniently chosen to be the angular magnification of the viewfinder telescope

relative to that of the original telescope,

θ

21

'.

'

12

f f

f f

M

(9)

The set of equations in Eq. (8) does not appear to have a solution that can be expressed in

closed form, even when using symbolic mathematical calculation software such as

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Received 20 Aug 2012; revised 5 Oct 2012; accepted 5 Oct 2012; published 12 Nov 2012

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