04020257.pdf

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 6, DECEMBER 2006

1555

Addressable Microlens Array to Improve Dynamic

Range of Shack–Hartmann Sensors

Hyuck Choo and Richard S. Muller

, Life Fellow, IEEE, Member, ASME

Abstract—

In this paper, we have demonstrated an addressable

array (5-by-5) of high-quality microlenses suitable for application

in a Shack–Hartmann (SH) sensor in a microoptical system. Spe-

cific lenses in the array can be addressed using a new selection

scheme (that we have designed, built, and tested) in which the me-

chanical resonant frequencies of individual lens-support carriages

are varied. Thus, by changing the frequency of the drive voltage, we

require only two electrical connections per row in the lens system

to identify the selected lens by its resonating focal image. We show

that using this lens-identification method will allow us to improve

the dynamic range of SH sensors by a factor of 12–46 above values

reported for conventional SH designs.

[2006-0015]

Index Terms—

Dynamic range, frequency addressing, microlens,

optical microelectromechanical systems (MEMS), Shack–Hart-

mann (SH) sensor.

OMENCLATURE

Overlapping area between moving and

fixed comb fingers.

Area of the top surface of the resonant

structure.

Overlapping area between the resonant

structure and substrate.

Damping factor.

Actuation distance.

Diameter of microlens.

Young’s modulus of elasticity of silicon.

Focal length of the lens.

Resonant frequency.

Gap between moving and fixed combs.

Gap between two parallel flexures.

Stiffness or spring constant.

Stiffness or spring constant of the combs

-direction.

Manuscript received February 7, 2006; revised June 27, 2006. This paper was

presented in part at the 2004 Solid-State Sensor, Actuator, and Microsystems

Workshop, Hilton Head Island, SCJune6–102004. Subject Editor C. Hierold.

The authors are with the Berkeley Sensor and Actuator Center, Department

of Electrical Engineering and Computer Sciences, University of California,

Berkeley, Berkeley, CA 94720-1774 USA (e-mail: hchoo@eecs.berkeley.edu).

Color versions of Figs. 3, 8(b), 9, 12, 13, and 15 are available online at http://

ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JMEMS.2006.886011

Stiffness or spring constant of the flexures

-direction.

Stiffness or spring constant of the flexure

-direction.

Maximum stiffness or spring constant of

the flexure in

-direction allowed in a

single row.

Length of combs.

Length of flexures.

Length of overlap between fixed and

moving combs.

Total mass of the microlens resonant unit.

Mass of the moving structure without lens

and flexures.

Mass of the flexures attached to the unit.

Mass of the lens.

The number of moving comb fingers.

Thickness of the device layer of the SOI

wafer.

Thickness of the buried oxide layer of the

SOI wafer.

DC driving voltage.

AC driving voltage.

Maximum dc-driving voltage before side

thrust occurs (at resonance).

Maximum dc-voltage before a side thrust

occurs (at stationary position).

Width of flexures.

Width of combs.

Initial overlap length between the fixed

and moving combs.

Desired actuation distance at resonance in

-direction.

Maximum actuation distance before a side

thrust occurs (at resonance) in

-direction.

Actuation distance at resonance in

-direction.

Permittivity of air.

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 6, DECEMBER 2006

Fig. 1. (a) Wavefront-slope measurement using microlens array: each microlens has its own subaperture consisting of approximately 40 CCD pixels (di

vided into

four quadrants), and the focal point of the microlens must be located within the assigned subapertures; (b) Limited dynamic range of a conventional Sh

ack

–

Hart-

mann sensor (left): a highly aberrated wavefront causes the focal points of microlenses #1 and #3 to become focused onto the subapertures assigned to m

icrolenses

#4 and #5, respectively, causing erroneous measurements.

Density of single crystal silicon.

Density of lens material.

Angular frequency

Angular resonant frequency

Viscosity of air.

Kinetic viscosity of air.

I. I

NTRODUCTION

HACK

–

Hartmann (SH) sensors are widely used in astro-

nomical telescopes and ophthalmic-analysis systems as

monitors for wavefront aberrations. They are fast, accurate, and,

in contrast to interferometers, generally insensitive to vibra-

tions. When they are used in conjunction with adaptive mirrors,

Shack

–

Hartmann sensors are able to improve the image quality

of astronomical telescopes by performing real-time corrections

on the wavefront aberrations that are inherently generated as

starlight traverses the earth

’

s atmosphere [1]. Shack

–

Hartmann

sensors have also proven to be the most suitable wavefront

monitors for ophthalmic-analysis applications (such as pre-

and/or post-LASIK surgery and keratoconus analysis) because

measuring the optical aberrations in illumination passing

through constantly moving human eyes requires fast measure-

ment speed and high accuracy [2]

–

[6].

In Shack

–

Hartmann systems, a microlens array dissects an

incoming wavefront into a number of segments [Fig. 1(a)] [7].

Each microlens in the array creates a focal spot within the as-

signed subaperture on the charge-coupled device (CCD) (typi-

cally made of 40 CCD pixels). Because light travels in a straight

path normal to the wavefront, the positions of these focal spots

are related to the average wavefront slope over each microlens

aperture. Thus the pattern of spots at the focal plane contains in-

formation about the spatially resolved waveform slope that can

be integrated to reconstruct the wavefront. The dynamic range

(the range of measurable wavefront slope) of a conventional

SH system has fundamental design limits that affect its perfor-

mance; an SH system produces false results if the curvature of

the wavefront being measured is too large [2]. Fig. 1(b) shows

one of these cases in which a focal point of one microlens, as a

result of extreme aberration in the incoming wave, moves into

an adjacent subaperture that has been preassigned to register the

focal point of another microlens.

Researchers have attempted to overcome this dynamic-range

limitation of SH systems using at least three methods: 1) by em-

ploying a modi

ed unwrapped algorithm [8], 2) by using an SH

array of microlenses with well-de

ned astigmatism [9], or 3)

by positioning a spatial-light modulator in front of the SH mi-

crolens array as a shutter [10]. Research showed that the

rst two

methods had limited practical use providing accurate measure of

wavefront aberration. Method 1) does not work with wavefronts

that exhibit localized aberrations of large magnitudes. Method

2) requires that the elliptical focal spots have enough space be-

tween them along the major and minor axes in order to obtain

proper measurements. Hence, the spatial density of the astig-

matic microlens array has to be much lower than that of a cir-

cular microlens array, and this in turn lowers the accuracy of the

sensor. Method 3), which employs a spatial-light modulator, is

also impractical on three grounds: the modulator absorbs a great

deal of light (at least 50% in the case of a liquid crystal dis-

play illuminated with unpolarized light); it increases the noise

in the measurement; and it introduces additional aberrations to

the wavefront being measured. In addition, spatial-light modu-

lators can have polarization dependences, and these modulators

are typically very expensive.

Nonetheless, expanding the dynamic range of Shack

–

Hart-

mann sensors is highly desired, especially in consideration of

their increasing uses in refractive surgery ($600 million market

in 2001) and in keratoconus analysis. In the case of refractive

surgery, the development of a transition zone (resultant from

scar tissues) at the boundary separating surgically treated and

untreated areas results in large optical aberrations [11] when the

CHOO AND MULLER: DYNAMIC RANGE OF SHACK

–

HARTMANN SENSORS

1557

Fig. 2. By making each microlens resonate individually, we can identify its

associated focal point, even if the focal point is located outside the assigned

subaperture.

tissue is examined. Also analyzing ophthalmic diseases such as

keratoconus (meaning cone-shaped cornea) requires large dy-

namic ranges and sensitivities that cannot be achieved by con-

ventional Shack

–

Hartmann sensors [2].

Using microelectromechanical systems (MEMS) technolo-

gies developed in the Berkeley Microlab, we have created

densely packed active microlens arrays in which each of the

lenses is designed so that it can be driven to resonate at a

predesigned frequency. When a lens resonates, its focal point

moves parallel to its motional direction [12], [13]; hence by

selecting the frequency of the driving voltage on a string of

parallel-connected lenses, we can select only the lens that is

resonant at the driving frequency. We can then identify the

focal point of that resonating lens by detecting a line instead

of a point image Fig. 2. To build the system, we have designed

the individual lens carriages for the array of lenses to have

separated natural resonant frequencies so that, by changing the

frequency of the drive voltage, we require only two electrical

connections per lens-carriage row to identify the selected lens.

With our design, a lens focal point can be identi

ed even

when it falls outside of its associated subaperture (usually 40

pixels for Shack

–

Hartmann sensors for ophthalmic analysis),

anywhere in the sensing array. This identi

cation will allow the

dynamic range of the Shack

–

Hartmann sensor to be dramati-

cally improved

—

a factor of 26 to 46 better than that achieved

in conventional Shack

–

Hartmann systems. In this paper, we dis-

cuss the design, fabrication, and experimental results on our ad-

dressable microlens array.

II. A

DDRESSABLE

ICROLENS

-A

RRAY

ESIGN

A. Design Objectives and Considerations for Addressable

Microlens Array

The design of our addressable microlens array for

Shack

–

Hartmann sensors has been guided by the following

objectives.

1) Maximize the clear aperture of the system (or microlens

area) by minimizing the areas for MEMS actuators and

electrical interconnects.

2) Assure that only the desired lens moves appreciably while

all other lenses in its row remain essentially stationary,

even when the lens carriage with the stiffest

exures

(highest resonant frequency) in the row is actuated with

the highest drive voltage.

The

rst objective is reached by designing and building the

lens-carriages using the most ef

cient surface-micromachining

capabilities available in our laboratory. Achieving the second

objective requires the simultaneous consideration of the fre-

quency responses of all the units in a single row and the analysis

of side instabilities of the resonating units. The side-instabilities

are caused by the electrostatic pull-in phenomena [14], which

we discuss in more detail later in this paper. The frequency

responses and side-thrust issues will determine the maximum

number of the MEMS-microlens units per row that can be reli-

ably addressed by our frequency-addressing method.

B. Layout and Dimensions of the Addressable-Microlens Array

Fig. 3 shows an enlarged view of an individual MEMS-mi-

crolens unit and the schematic diagram of our addressable-mi-

crolens array.

In order to utilize the area inside the unit rectangular cell

(1360 by 1460

)ef

ciently, the microlens is placed at the

center of the cell, the two truss-joined double

exures are placed

at the top and bottom of the cell, and comb-

ngers (numbering

172 moving and 184

xed) are concentrated between the two

exures, around the microlens [Fig. 3(a)], inside the cell. The

comb-

ngers are grouped into upper and lower comb sets, as

shown in Fig. 3(a). The upper comb sets are mirror images of

the lower comb sets re

ected across the

-axis. The truss-joined

double

exures have been chosen to maximize pliability along

the actuation directions of the resonant structures as well as to

stiffen their resistances to undesired sideway motions.

Each row contains

ve adjacent microlens-resonant units de-

signed to have

ve different mechanical-resonant frequencies.

The frequencies are varied by decreasing the support-

exure

lengths from 900 to 500

m in steps of 100

m, from the left

(Unit 1) to the right (Unit 5) [Fig. 3(b)]. Using our frequency-ad-

dressing method, we need only a single pair of interconnects per

row to select and energize each unit, reducing and simplifying

the area and complexity necessary for alternative selection de-

signs. A 5-by-5 addressable array is then obtained by stacking

ve identical rows (Row1

–

Row5), as shown in Fig. 3(b). The di-

mensions of the MEMS-microlens resonant structures are sum-

marized in Table I, while other relevant material parameters are

listed in Table II. The reasons for choosing the listed values for

the dimensions will be clari

ed in the following sections.

C. Design of MEMS Resonators With Electrostatic Actuators

In order to assure the successful, distinctive resonant mo-

tion of each MEMS-microlens unit, the following requirements

must be met. (Please refer to Fig. 4.) First, each unit must be

able to achieve

m amplitude at resonance stably and

without appreciable sideway motions. Secondly, when the unit

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 6, DECEMBER 2006

Fig. 3. Schematic diagrams showing features of addressable-microlens array. (a) Individual resonant unit. (b) Our resonant-frequency addressing

method requires

only a single pair of electrical lines per row to control each unit individually. Rows 1

–

5 are identical; each row contains

ve MEMS-microlens units having

different resonant frequencies

)

Fig. 4. Examples of frequency response of MEMS-microlens units in a row: (a) three resonant peaks suf

ciently spaced for clear identi

cation (higher Q); (b)

resonant peaks suf

ciently spaced for clear identi

cation (lower Q); and (c) resonant peaks insuf

ciently spaced for identi

cation: when Unit 1 is at resonance,

Unit 2 will also show considerable movements, making it dif

cult to identify the units.

TABLE I

ELEVANT

ARAMETERS OF THE

MEMS-M

ICROLENS

NITS

TABLE II

ELEVANT

ATERIAL

ARAMETERS FOR THE

MEMS-M

ICROLENS

NITS

with the highest resonant frequency (which has the stiffest

ex-

ures and therefore requires the highest driving voltage) achieves

m resonant amplitude, all other units must move only

negligibly and be free from any undesired side thrust. Thirdly,

the resonant peak of each MEMS-microlens unit should be suf-

ciently separated in frequency from the resonant peaks of the

other units in the same row.

A side-thrust mentioned in the

rst and the second require-

ments is caused by the electrostatic pull-in phenomenon [14],

which is illustrated in Fig. 5. The moving combs are sometimes

not perfectly centered between the

xed combs due to the pro-

cessing variations Fig. 5(c). And, even if the combs were ini-

tially aligned perfectly, they can slightly deviate from the ideal

line of actuation when the structures are actuated or some ex-

ternal vibrations are present. This slight misalignment results

in an unbalanced net electrostatic force in the direction (

-axis)

perpendicular to the desired actuation (

-axis) [Fig. 5(c)]. When

the changes in these electrostatic forces with respect to

be-

come larger than the stiffness of the

exures along the

-axis,

the moving comb-

ngers will bend and in all likelihood stick to

the

xed combs, causing the proper operation of the structure

to fail, as shown in Fig. 5(d). We call the voltage at which the

structure begins to fail in this way the

side-thrust voltage

There are two different cases of side thrust that we consider.

The

rst case, which we call

dynamic side thrust,

may occur

CHOO AND MULLER: DYNAMIC RANGE OF SHACK

–

HARTMANN SENSORS

1559

Fig. 5. (a) Sketches of the upper half of a MEMS-microlens unit; (b) perfectly aligned

xed and moving combs; (c) misaligned

xed and moving combs

—

the

gaps on the right side of the moving combs are smaller than those the gap on the left side of the moving combs, causing unbalanced electrostatic force in t

x-direction. (d) The force

generated by the misaligned combs causes the unit to shift to the left by

. If the change in

is larger than the stiffness of the

exures in

-direction,

becomes as large as

, and the moving-comb

ngers become suf

ciently displaced to cause electrical contact with the

xed-comb

ngers, shorting out the drive voltage.

to the unit at resonance when its drive voltage is increased

to achieve the intended resonant amplitude. The second case,

stationary side thrust,

occurs when the unit with the highest

resonant frequency is driven to the desired resonant amplitude

while the others are stationary. We need to consider them sepa-

rately because the overlapping areas between the moving- and

xed-comb

ngers remain constant for stationary side thrust

yet change in the case of dynamic side thrust. For stationary

side thrust, some of the other lower resonant-frequency units

may experience side thrust because the highest frequency unit

has the stiffest

exures and requires the highest drive voltage.

This high drive voltage is applied to all the units in the row,

possibly causing one or more of them to move in an undesired

direction and to fail.

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TABLE III

REDICTED

ESONANT

REQUENCIES AND

UALITY

ACTORS OF THE

IVE

MEMS-M

ICROLENS

ESONANT

NITS IN A

Considering both types of failures and the needed selectivity

among the lenses in a given row, we see that the number of units

in a row is determined by (a) the upper and lower limits on reso-

nant frequencies set by the side-thrust issues and (b) the quality

factors of the resonant units in the row, which determine the

spacing needed between adjacent units in the frequency domain

for clear distinction.

To analyze the effects of these limitations, we begin by for-

mulating expressions for the resonant frequencies, quality fac-

tors, and resonant amplitudes of the lens units. Then we con-

sider the range of resonant frequencies allowed in a single row

as set by the physical dimensions of the unit cell as well as by

the side-thrust issues.

1) Calculations of Resonant Frequencies, Quality Factors,

and Resonant Amplitudes:

The resonant frequency of each

MEMS-microlens unit is [15]

(1)

where

is [16]

(2)

The stiffness

of the

exures is calculated using rectangular

beam theory [17]

(3)

From (1) and (3), we see that increasing the stiffness

by re-

ducing the

exure length

increases the resonant frequency

The mechanical quality factor

for the resonant carriages is

(4)

The damping factor

is calculated by summing i) Couette-

damping between the

xed and moving comb-

ngers, ii) Cou-

ette-

ow damping between the resonant structure and the sub-

strate, and iii) Stokes-

ow damping over the reso-

nant structure [18]

(5)

Using the fundamental resonant frequencies and the Q fac-

tors, we predict the frequency response of the microlens reso

nant structures in a row as [15]

(6)

In (6),

is the angular frequency of the drive voltage and

the angular resonant frequency of the unit under consideration.

As shown in Fig. 3, each MEMS-microlens unit has two sets of

comb

ngers: an upper and a lower set. The upper and lower

sets actuate the MEMS-microlens unit upward and downward,

respectively. Each of these sets has an equal number of paired

xed- and moving-comb

ngers. Hence, dc voltage simultane-

ously applied to both upper and lower comb sets causes balanced

forces and no displacement; only an ac voltage, that is applied

to the upper and lower comb sets with a 90

-phase lag one from

the other, will cause displacement. In this case, the equation for

the resonant displacement becomes

(6-1)

For cases in which

is much larger than

can be

further simpli

ed as

(6-2)

The designer must consider (6-1) when it is applied over the

frequency range of interest in order to assure that each unit in

a given row achieves the desired amplitude at its resonant fre-

quency while movements in the other units in the row are negli-

gible at that frequency. The selected unit must also resonate at

the desired amplitude without suffering from excessive dynamic

side thrust. At resonance, the amplitude is

(7)

For cases in which

is much larger than

, the expression

for the maximum amplitude at the resonant frequency can be

approximated as

(7-1)

Turning now to the

dynamic side thrust

issue, we calculate the

maximum attractive electrostatic force between the moving and

xed combs that causes side-thrust at the resonant frequency

[14]

(8)

CHOO AND MULLER: DYNAMIC RANGE OF SHACK

–

HARTMANN SENSORS

1561

Fig. 6. (a) Predicted frequency responses of the MEMS-microlens units and (b) graph representing the data in Table IV to emphasize the selectivity of t

he me-

chanical-resonance method.

TABLE IV

REDICTED

MPLITUDES FOR THE

MEMS-M

ICROLENS

NITS AT

IFFERING

RIVE

REQUENCIES

OLD

HARACTERS

NDICATE THE

ESONANT

NIT

(

MPLITUDE

)

In (8), the number of comb

ngers

is divided by two be-

cause

is sinusoidal and its peak voltage is applied either to

the upper or to the lower comb each half-cycle. The stable op-

eration of the resonant unit requires that

(9)

In (9),

is the effective stiffness of the truss-joined double-

exures in the

-direction; this parameter can be calculated by

considering the slope developed at the end of the

exure beams

when stiction takes place [17]

(10)

When the drive voltage exceeds the side-thrust voltage

, the comb drive becomes unstable, leading the

moving comb

nger to stick to its

xed counterpart. If we ex-

press

using (7-1) in (9) and assume a reasonable value for

(for example,

), we can solve for

(11)

where

We now use (11) to express

in (7) and calculate the max-

imum displacement that the resonant unit can achieve before ex-

periencing electrostatic pull-in

(12)

For stable operation of MEMS-microlens units, this maximum

displacement before side-thrust must be larger than the desired

resonant amplitude.

2) Lower and Upper Limits on Resonant Frequencies:

The

lower limit on the resonant frequencies is related to the physical

size of the rectangular unit cell. In our design, the maximum

length of

exures that can be placed inside the unit cell is 1250

m, which gives rise to the lowest resonant frequency of 0.99

kHz. However, to provide a margin of safety (because of pos-

sible variations in voltage values as well as tolerance limits in

surface micromachining), it is reasonable to set the maximum

length (and corresponding minimum resonant frequency) to 900

m and 1.56 kHz, respectively.

After we have the

exure length for the lowest frequency

unit, we can calculate the

exure length for the highest fre-

quency unit based on the stationary side-thrust condition of the

lowest frequency unit. The worst case that we need to con-

sider occurs when the highest frequency unit (unit 5 in Fig.

3) is resonating. In this condition, we need to assure that the

lowest frequency unit, which has the most pliant

exures, re-

mains stationary and stable. Hence we

rst calculate the sta-

tionary side-thrust voltage for the lowest frequency unit at the

stationary (rest) position. This side-thrust voltage of the lowest

frequency unit is the highest voltage that can be applied to the

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JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 6, DECEMBER 2006

Fig. 7. Fabrication process of addressable microlens array.

1) Grow a 1-



m-thick thermal-silicon dioxide layer on a SOI wafer.

2) Pattern the layer to make a mask that will later de

ne combs,

exures,

supports, and lens frames.

3) Deep reactive ion etch (DRIE) trenches that will be used to form an-

chors and electrical connections between the device layer and the han-

dling layer of the SOI wafers.

4) Deposit a 0.5-



m-thick low-pressure chemical vapor deposition

(LPCVD) polysilicon layer to create electrical contacts from the device

layer to the handling layer (which serves as a ground). The polysilicon

layer also protects the oxide mask.

5) DRIE circular trenches in the device layer. These trenches will serve as

wells for droplet microlenses later.

6) Deposit (using LPCVD) a 2-



m-thick silicon nitride layer (tensile stress,



250 MPa) and pattern the layer.

7) DRIE silicon parts (combs,

exures, supports, and lens frame) using the

silicon dioxide mask layer de

ned in step 2).

8) Open the backside of the wafers using DRIE to make clear apertures for

microlenses.

9) Release the devices in concentrated HF.

10) Make microlenses using polymer-jet printing technology. The boundary

of the trench de

nes the diameter of the lens.

common electrical interconnects in the row without causing sta-

tionary side thrust in any of the units. Then, using the stationary

side-thrust voltage

of the lowest frequency unit at the

stationary position, we calculate the minimum

exure length of

the highest frequency unit that will allow

m displace-

ment at resonance when driven at a voltage

of the

lowest frequency unit

(13)

(14)

Solving (9) for

, we obtain

where

(15)

For

m and

is 44.74 V. Using

(7-1), we now calculate the maximum stiffness of the

exures

that can still achieve

m resonant amplitude

at this voltage

(16)

The damping factor

[(5)] increases gradually as the

exure

lengthens; however, for resonant frequencies between 1

–

kHz, the change in

is typically less than 10% of its original

value in our design. Hence, to simplify calculation, we assume

that

xed at 0.49

s/m. Assuming

V, w e

obtain

N/m, and the corresponding maximum

resonant frequency and quality factor are 5.84 kHz and 437.91,

respectively. Using the numerical value of

in (3) and

solving for

, we obtain

(17)

Equation (17) shows that the minimum length of the

exures

allowed in a row (that can achieve

m displacement at

resonance without causing side-thrust in low-frequency units) is

352

m. This minimum length determines that the upper limit

on the resonant frequencies allowed in the row [using (1)

–

(3)]

is 5.84 kHz. As before, if we provide a safety factor (e.g., select

instead of 352

m as the minimum

exure length), we

calculate an upper limit for the resonant frequency of 4 kHz.

3) Frequency Response of the Resonant Units in a Single

Row: Resonant Frequencies and Quality Factors:

After

choosing the design values that bracket upper and lower reso-

nant frequencies of the MEMS-microlens units in a given row,

we calculate the number of units having addressable resonant

frequencies that can be placed in the row.

We predict the frequency response of the MEMS-microlens

resonant structures in a row using (18) [15]

(18)

CHOO AND MULLER: DYNAMIC RANGE OF SHACK

–

HARTMANN SENSORS

1563

Fig. 8. Microlens fabrication process: (a) fabrication diagram and (b) fabrication setup in our laboratory.

Fig. 9. Microlens fabrication process: stroboscopic observation

—

the focal length is controlled by varying the volume of the microlens.

Fig. 10. SEM picture of the fabricated addressable microlens array (a) before and (b) after microlens fabrication.

Equation (18) can be used to ensure that at the resonant fre-

quency of the unit of interest, the other units in the row do not

show any signi

cant movement.

As a design example, we fabricated a lens array in which

MEMS-microlens units (as described in Table I) were placed

in a row having the dimensions indicated in Table III. Predicted

resonant frequencies and mechanical quality factors for the units

are also given in Table III, while in Table IV, we show predicted

amplitudes for the units when they are driven at

ve different

drive frequencies and voltages. Theory predicts that when a des-

ignated unit is at full resonance reaching amplitudes of

the other four units move less than

m, as shown in Fig. 6.

The appropriate spacing between neighboring resonant frequen-

cies together with stability condition determines the maximum

number of units that can be placed in each row for a given max-

imum frequency of driving voltage.

III. F

ABRICATION OF

DDRESSABLE

ICROLENS

RRAY

Our addressable-microlens array is fabricated in two

steps: A) the MEMS-microlens carriages are built using a

Berkeley Sensor and Actuator Center (BSAC)-conventional

silicon-MEMS process and B) microlenses are formed on

the MEMS carriages using polymer-jet printing technology

developed in our laboratory [19].

A. Fabrication of MEMS-Microlens Carriages

Steps in the fabrication process of MEMS-microlens car-

riages are shown in Fig. 7 and described in the

gure caption.

In order to make high-quality lenses using polymer-jet

printing technology, it is necessary to form very

at, optically

transparent diaphragms on the MEMS carriage structures. We

have used LPCVD-deposited silicon nitride thin-

lm mem-

branes [step 6) in Fig. 7] and found them to be excellent for

this purpose. As demonstrated in previous work [20], [21], low

tensile-stress (

250 MPa) LPCVD-deposited silicon nitride

membranes (5 mm squares) are virtually

at (radius of curva-

ture

51 m) and physically very robust [22]. Silicon nitride

membrane also show excellent spectral transmission in the

visible region (75

–

95%). These excellent qualities combine

to make the membranes very good choices for microlens sub-

strates.

1564

JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 15, NO. 6, DECEMBER 2006

Fig. 11. SEM picture of the fabricated individual MEMS-microlens unit before and after microlens fabrication.

Fig. 12. WYKO measurement of low tensile-stress (250 MPa) nitride-mem-

brane surface pro

le: very

at (radius of curvature



3 m) within 200



m radius.

B. Direct Fabrication/Integration of Microlenses on

MEMS-Carriages

Fabrication of high-quality droplet microlenses using hy-

drophobic effects [22] or polymer-jet printing technology [23],

[24] has been reported by other researchers. In earlier research,

we reported the fabrication of high-quality microlenses with

excellent uniformity by combining the hydrophobic-effect

method with polymer-jet printing technology [19]. To form the

SH lens array, we repeated this established method depositing

the polymer lenses on preformed silicon nitride substrates

supported by the individual lens carriages.

The photograph on the right-hand side of Fig. 8 shows the mi-

crolens-fabrication setup in our laboratory. The microlenses are

precisely formed by polymer-jet printing on 2-

m-thick silicon

nitride layers that are uncovered by etching circular wells (20

m in diameter) into the device layer of SOI wafers. The bound-

aries of the circular wells precisely de

ne the lens diameters,

and surface tension in the polymer creates a high-quality optical

surface. The polymer-jet printing head used in our system is the

Microfab MJ-AT-01-40, which operates at room temperatures.

The MJ-AT-01-40 requires that the viscosity of the printed ma-

terial not exceed 40 cps . We used Epoxy Technology

’

uv-cur-

able

Epo-Tek OG146, which meets this requirement at room

temperature.

In addition to its low viscosity, Epo-Tek OG146

possesses excellent optical properties: more than 95% spectral

transmission after curing in the 0.4

–

m (visible to near-in-

frared regions) range and a refractive index of 1.51.

Optical properties such as the focal length for a microlens are

adjusted by controlling the volume of deposited polymer mate-

rial [19]. The total microlens volume is the sum of the spher-

ical part and the cylindrical part, as shown in Fig. 8(a). To give

Microfab Technologies, Inc., Plano, TX.

Epoxy Technology, Billerica, MA.

an example: we fabricate a 2-mm-focal-length microlens on the

MEMS-microlens carriage by depositing 2.98

(or

29.8 nl) of the microlens material. Since the polymer-jet printing

head generates a droplet of 0.025 nl, we need to deposit 1192

drops to fabricate a microlens having the required properties on

the MEMS carriage.

IV. E

XPERIMENTAL

ESULTS AND

ISCUSSION

Examples of our 5

5 addressable-lens arrays, fabricated

using SOI wafers, are pictured in the scanning electron micro-

scope (SEM) photographs shown in Figs. 10 and 11. Each ad-

dressable unit (1.5 mm

) contains one 800-

m-diameter mi-

crolens with lens-support carriage and actuators.

A. Microlens

Using WYKO-NT3300, we measured the surface pro

les of

the low-stress (

250 MPa) tensile-silicon nitride-membranes

and microlenses (EFL

mm) (Figs. 12 and 13). Within a

200-

m radius, the membranes are virtually

at (radius-of-cur-

vature

3 m) (Fig. 12). Near the edge, the membrane pro

les

deviate slightly from ideal

at surfaces, but the maximum devi-

ation across its 800

m diameter is still lower than 0.5

m. The

average surface roughness is measured at 8.7 nm.

Using our polymer-jet printing technique in circular wells,

we have been able to produce microlenses with effective focal

lengths (EFLs) ranging from 1.94 to 7.48 mm as adjusted

by controlling the deposited polymer volumes forming the

microlenses. Fig. 12 shows the surface pro

le of a microlens

and its deviation from that of an ideal circle. The

microlens surfaces closely approximate a circle having radius

2.2 mm.

For our addressable-microlens array, microlenses having a

designed focal length of 2.0 mm were fabricated. The 25 fab-

ricated microlenses have an average EFL of 2.09 mm, and the

peak-to-peak variation in EFL is

7%.

B. Mechanical Performance

The measured mechanical resonant frequencies of the

MEMS-microlens units 1 through 5 (microlens EFL

mm) are 1.31, 1.58, 1.98, 2.48, and 3.49 kHz, re-

spectively. The corresponding mechanical Q-factors (microlens

EFL

mm) are 65.4, 105.1, 142.1, 174.8, and 205.2.

Across the same chip, the maximum variation in resonant fre-

quencies of

ve identical units is less than 5%. All units achieve