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Lawrence Berkeley National Laboratory
Lawrence Berkeley National Laboratory
Peer Reviewed
Title:
Measurement of lateral charge diffusion in thick, fully depleted, back-illuminated CCDs
Author:
Karcher, Armin
Bebek, Christopher J.
Kolbe, William F.
Maurath, Dominic
Prasad, Valmiki
Uslenghi, Michela
Wagner, Martin
Publication Date:
06-30-2004
Publication Info:
Lawrence Berkeley National Laboratory
Permalink:
http://escholarship.org/uc/item/2pp8s12h
Keywords:
CCD diffusion fully-depleted
Abstract:
Lateral charge diffusion in back-illuminated CCDs directly affects the point spread function
(PSF) and spatial resolution of an imaging device. This can be of particular concern in thick,
back-illuminated CCDs. We describe a technique of measuring this diffusion and present PSF
measurements for an 800x1100, 15 mu m pixel, 280 mu m thick, back-illuminated, p-channel CCD
that can be over-depleted. The PSF is measured over a wavelength range of 450 nm to 650 nm
and at substrate bias voltages between 6 V and 80 V.
Abstract-- Lateral charge diffusion in back-illuminated CCDs
directly affects the point spread function (PSF) and spatial
resolution of an imaging device. This can be of particular
concern in thick, back-illuminated CCDs. We describe a
technique of measuring this diffusion and present PSF
measurements for an 800×1100, 15 µm pixel, 280
µ
m thick,
back-illuminated, p-channel CCD that can be over-depleted. The
PSF is measured over a wavelength range of 450 nm to 650 nm
and at substrate bias voltages between 6 V and 80 V.
I. INTRODUCTION
The spatial resolution of a CCD is determined by pixel size
and lateral charge diffusion. The charge diffusion can be of
concern in back-illuminated devices due to the distance
between the point of charge generation and charge collection.
Thick, back-illuminated devices generally have higher
quantum efficiencies over a broader range of wavelengths, as
well as less fringing at near-infrared wavelengths, making
them useful for a variety of astronomy applications. But thick
devices can have large lateral diffusion unless carefully
designed. In most back-illuminated CCDs, self depletion
typically occurs within a ∼10 µm region of the front side
leaving a significant non-depleted region at the backside and
this results in a point spread function rms width comparable
to the thickness of this field free region, typically of order
10 µm.
The Lawrence Berkeley National Laboratory (LBNL) CCD
technology [1]-[3] allows control of lateral charge diffusion.
The CCDs are fabricated on 200 to 300 µm thick weakly-
doped n-type substrates with donor densities of ∼1011 /cm 3
(>5 k Ω-cm). The substrate can be fully depleted, even over
depleted. The operation of the CCD including clocking and
output source follower can be optimized for good charge
Manuscript received November 2003; revised May 2004.
This work was supported by the Director, Office of Science, of the U.S.
Department of Energy under Contract No. DE AC03-76SF00098.
C. J. Bebek, A. Karcher, W. F. Kolbe, and V. Prasad are with the Lawrence
Berkeley National Laboratory, Berkeley, CA 94720-8164 USA (telephone: 510-
486-6447, e-mail: cjbebek@lbl.gov).
D. Maurath and M. Wagner are with the Department of Sensorsystem
Technology, Fachhochschule Karlsruhe - Hochschule für Technik, Karlsruhe,
Germany.
M. Uslenghi is with the Instituto di Fisica Cosmica, Milan, Italy.
transfer, well depth, and gain independent of the substrate
bias voltage. When fully depleted, no field free region exists
and charges are directed by an electric field during their entire
drift time to the collection well. In this paper, we describe a
technique of measuring the lateral charge diffusion and
present experimental PSF results for an LBNL CCD.
Our long term goal is to populate the focal plane of a
diffraction-limited telescope with 109 pixels covering the
wavelength range 0.35 to 1.0
µ
m. For the same angular
coverage on the sky, a small-pixel-size CCD will require less
instrumented area but the lateral charge diffusion must be
commensurate with the pixel size so as not to significantly
degrade the telescope PSF. To maintain good red response we
want to maintain the CCD thickness at 200
µ
m and still
achieve an rms PSF of 4
µ
m. Since the authors are interested
in photometry of point-like objects, we choose to use PSF as a
measure of lateral charge diffusion impact rather than
modulation transfer function.
II. MEASUREMENT PRINCIPLE AND TECHNIQUE
We measure the charge profile of a point light source on the
CCD to determine the PSF. Our measurement technique is
based on the Foucault knife-edge technique. Instead of a
physical knife edge, we select a grid of pixels and measure the
variation of the total charge in the grid as the beam is scanned
across a grid edge, a virtual knife edge. As shown in Fig. 2,
the grid (integration region) is chosen such that initially the
beam is completely contained within it. At the end of the scan,
the beam lies outside the grid. The variation of the total
charge in the integration region as a function of the beam
position relative to the grid edge yields the charge profile in
the scan direction as shown in the top of Fig. 3. The charge
profile is one of two forms depending on the depletion regime,
(1a) for under depletion where some fraction of the drift path
is field free and (1b) for over depletion where the charges
experience no field-free drift region [3], [4]
368.1
/
cosh/1
/
)(
)( =
′
⎟
⎠
⎞
⎜
⎝
⎛−
′
−
−= ∫
∞−
kxd
k
cx
k
ba
axQ x
σπσ
(1a)
xd
cxba
axQ x′
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛−
′
−−
−= ∫
∞−
2
2
2
)(
exp
2
)(
)(
σ
σπ
(1b)
Measurement of Lateral Charge Diffusion in
Thick, Fully Depleted, Back-illuminated CCDs
Armin Karcher, Christopher J. Bebek, Member, IEEE, William F. Kolbe, Dominic Maurath,
Valmiki Prasad, Michela Uslenghi, Martin Wagner
where a is the asymptotic charge value when the beam is
fully contained in the integration-region, b is the asymptotic
value when the beam is fully outside the integration region, c
is the beam-center location where the integrated charge is half
of ba −. Ideally, b would be zero but it accommodates
electronics offsets. σ is the rms of the charge profile in the
gaussian regime of (1b) and
k
is defined so that
xd
x
xd
k
x
k′
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛′
−
=
′
⎟
⎠
⎞
⎜
⎝
⎛′∫∫ −−
σ
σ
σ
σ
σ
σπ
σπσ
2
2
2
exp
2
1
/
cosh/1
/
1 (2)
The derivative of the integral charge profile contains the
combined shapes of the source beam and the CCD response
shown in the bottom of Fig. 3. The advantages of this
technique over other approaches are independence of the pixel
size and no scattering from a physical knife edge. The
derivatives of (1a) or (1b) are fit to the data.
III. EXPERIMENTAL APPARATUS
A schematic of the experimental setup is shown in Fig. 4.
The CCD is mounted in a liquid nitrogen cooled dewar that
has been fitted with a thin, wide-band anti-reflection coated
window and a mechanical shutter. The dewar is evacuated to
∼10 -7 torr and the CCD is cooled to 133 K. The temperature
is regulated to an accuracy of about 1 K.
A small diameter light source is needed to minimize its
contribution to the charge profile in the CCD. An intense
beam is needed to decrease the statistical uncertainties in the
measurement. To achieve this, we use a GE 1493 tungsten
bulb operated at ~7 W behind a multi-lens collimator system.
The collimated light beam passes through a filter wheel
consisting of a set of Corion 70 nm bandwidth interference
filters. The beam is focused using a convex lens onto an
optical fiber that transmits the light to a pinhole projector.
The pinhole projector is comprised of a 25.4 mm long brass
tube that encloses a 10 µm diameter pinhole and a 5x long-
working-distance Mitutoyo objective. The latter has a working
range between 450 nm and 650 nm and a depth of focus of
∼30 µm. The inner surface of the projector tube is threaded
and blackened to reduce scattered light in the projected beam.
Light-tight rubber bellows are placed between the projector
and the dewar to prevent ambient light from reaching the
CCD.
The pinhole projector is mounted onto an x-y-z translation
stage, where the x-y plane is carefully aligned to the CCD
plane, with the x-axis parallel and y-axis perpendicular to the
CCD rows. The dewar is kinematically mounted to an
aluminum plate that, along with the projector translation
stage, sits on a Newport isolation table.
Projector x-y motions are implemented with stepper motors
with step sizes of 0.4 µm. The position of the projector is
read out using a non-contact linear optical encoder with an
accuracy of about 0.1
µ
m. Movement in the z-direction is
needed to focus the beam at the CCD surface and is performed
manually using two micrometer screws, one for rough focus
adjustment and the other for fine adjustment (1
µ
m/division).
A modified Astronomical Research Cameras Gen II
controller is used to read out and control the operation of the
CCD. A timing board generates the clock sequences and a
clock driver board provides various programmable voltages
for CCD operation. A video processor board filters, amplifies
and digitizes the CCD output. The control of the shutter
exposure time, projector x-y motion, linear encoder operation,
and temperature adjustment are performed using the
controller utility board. Java-based controller software
manages data-taking, while IDL-based software is used to
process and analyze the data.
IV. EXPERIMENTAL PROCEDURE
With the setup in Fig. 4, the charge profile is determined by
moving the focused beam across the surface of the CCD in the
x and y directions, corresponding to the rows and columns of
the CCD, respectively. The beam is scanned across the CCD
in 1.2 to 1.4
µ
m steps, with larger step sizes used for lower
substrate bias voltages. At each step, a 0.5-3 s exposure is
taken. The shutter exposure time and lamp intensity are
optimized to minimize statistical uncertainties while ensuring
that there are no saturated pixels. Each scan covers a distance
of 16-20 pixels, sufficient for measuring the charge profile at
different points along the CCD. The data collection and
analysis procedures are described below.
A. Projector beam profile
A modified setup of the apparatus in Fig. 4 is used to
measure the pinhole projector beam profile. A physical knife
edge and a photomultiplier tube (PMT) are placed in front of
the dewar. The beam is focused on the knife edge and the total
current in the PMT is measured as the pinhole projector is
scanned across the knife edge. The variation of the PMT
current with scan position is fitted to (1b) to extract the
intrinsic beam width. The procedure was performed at the
three wavelengths used in the lateral charge diffusion
measurement. The beam width measurements are shown in
Table I. The wavelength-averaged rms beam width, beam
σ, is
1.3
±
0.1
µ
m.
B. z alignment – focusing
To align the system, it is first necessary to focus the beam
on the CCD. This is accomplished by moving the projector in
the z-direction until the beam spot size on the CCD is
minimized. The ratio of the charge in the pixel with the
maximum charge to its neighboring pixels serves as a measure
of beam focus. To focus the system properly, we apply a large
substrate bias (∼60 V), thus depleting the substrate fully and
reducing lateral charge diffusion. The perpendicularity of the
projector axis to the CCD surface is checked by verifying that
the beam remains focused during an x or y scan across the
CCD.
C. x-y alignment
The x-y alignment of the CCD and projector is determined
by centering the beam on a pixel and then comparing the ratio
of charges in the two rows or columns adjacent to the row or
column containing the central pixel as the beam is scanned in
the x or y direction. A variation in the ratio of charges with
the scan position indicates a misalignment between the
projector motion and the CCD. The substrate bias voltage is
reduced to ∼40 V during these scans so that there is
appreciable charge in the pixels surrounding the central pixel.
The beam is scanned across ~10 pixels in 1.2 µm steps and
3 s exposure images are acquired. After aligning the system
using the x-y-z translation stage, we used a Monte Carlo
technique to extract the beam position variation during the
scan from the charge distribution variation. We find a typical
1 µm linear y-drift per 100 µm x motion and a
±
2.5
µ
m
oscillatory x-motion per 100 µm y motion.
D. Image offset level
Before processing each image, the quality of each image is
checked. Images without data-taking problems and cosmic
rays are processed by subtracting an overall image offset and
correcting for inter-pixel gain variations. We measure the
average offset per image from a square annular region in the
CCD that is illuminated with the beam. The rms uncertainty
in determining the offset is included in the total charge
measurement uncertainty in the integration region.
E. Inter pixel gain variation
After subtracting the offset from each image, we correct for
inter-pixel gain variation. The inter-pixel response is
measured by defocusing the beam such that it illuminates the
region of the CCD that we are investigating. To reduce the
effect of spatial variations in the unfocussed beam, the inter-
pixel response is obtained by averaging a series of dithered
and rotated images. We measure the pixel-to-pixel variations
for three wavelengths (450 nm, 550 nm, and 650 nm) and
find them to be ∼5%.
F. Image normalization
Fig. 5 shows that the total charge collected on the CCD
varies by ∼5% during a scan. This is due to variations in the
lamp-intensity and sub-pixel response. To correct for these
variations, we normalize the total charge in the integration
region to the total charge collected on the CCD for each
image.
V. EXPERIMENTAL RESULTS
We measured the lateral charge diffusion for an 800
×
1100,
15
µ
m pixel, 280
µ
m thick, back-illuminated CCD that was
fabricated at LBNL Micro Systems Lab. The PSF was
determined at ten different substrate bias voltages between 6 V
and 80 V and at three wavelengths: 450 nm, 550 nm, and
650 nm. Scans were performed in four directions,
±
x and
±
y, over a 200
×
200-pixel region of the CCD. Typical
measured charge profiles are shown in Fig. 6 for a few
substrate bias voltages.
The charge profile width, CCD
σ, is defined such that 68%
of the charge lies within CCD
σ± of the beam center. To
determine CCD
σ, we fit the rate of variation of the charge in
the integration region with respect to the beam position as
shown in Fig. 3. We fit (1a) for partially depleted
measurements, sub
V<15 V, and (1b) for fully-depleted and
over-depleted measurements.
We extract the PSF, diff
σ, from the relation
222 beamCCDdiff σ−σ=σ (3)
Since beam
σ is much smaller than the CCD
σ results shown
later, the PSF measurement is insensitive to the uncertainties
in the intrinsic beam size.
diff
σ was measured for different integration region sizes
and positions. For each substrate voltage, wavelength, and
scan, diff
σ had a typical statistical uncertainty of ∼0.05
µ
m.
For each substrate voltage and wavelength, the diff
σ’s were
distributed with an rms of ∼0.5
µ
m. This is included as one
of the systematic uncertainties in the measurements.
The results of the PSF measurements are shown in Fig. 7
and are presented in Tables II, III, and IV. Errors quoted
contain both statistical and systematic uncertainties. We do
not observe any significant difference in diff
σ at wavelengths
between 450 nm and 650 nm nor between x and y scan
directions. This is not surprising since the difference between
the absorption lengths in silicon at 450 nm and 650 nm is
only 2.7
µ
m. diff
σ is seen to decrease rapidly with increasing
substrate voltage in the partially-depleted region.
Fig. 7 shows a fit to the low voltage data based on the one-
dimensional analytical model in [3], equations (12) and (13),
)VV(
qN
yjsub
D
Si
Ddiff −
ε
−=σ 2 (4)
where D
y is the substrate thickness , Si
ε is the permittivity
of silicon, q is the electron charge, D
N is the donor density
in the bulk substrate, sub
V is the substrate bias voltage, and J
V
is the average channel potential. A fit yields J
V=-1.4
±
0.5 V
and D
N=(3.1
±
0.2)
×
1011 /cm 3. This donor density
corresponds to a bulk resistivity of ∼13.8 k Ω-cm, consistent
with the bare silicon wafer resistivity of ~10 kΩ-cm.
For the high voltage data, the theoretically diff
σ
approaches the constant-field result [2], [3]:
J
V
sub
VD
y
q
kT
diff −
⋅
=σ
2
2 (5)
where T is the absolute temperature and
k
is the Boltzmann
constant. The dashed line at high substrate voltages in Fig. 7
is (5) with J
V determined by the low voltage fit. We note a
consistent underestimate of the measured diffusion by this
procedure.
We used the same scan images as those used to determine
the charge profile to measure the accuracy of the x-y position
encoders. We measured the position of the center of each pixel
and the distance between the pixel centers for substrate
voltages greater than 44 V. The center of each pixel is
determined by fitting a Gaussian to the distribution of the
fraction of total charge in the central pixel as a function of the
encoder position. Fig. 8 shows the fractional charge in several
adjacent pixels during a scan. The distribution of the distance
between pixel centers is shown in Fig. 9. We observe that the
mean pixel spacing is different for scans in the row and
column directions and that there is indeed a trend in the pixel
separation measurements for scans in the ±y directions. The
cause of this trend and the differences between scan directions
is not understood at the moment. Combining row and column
scans, the mean pixel separation is 15.0 ±0.5
µ
m. This 3.3%
uncertainty in the encoder position measurement is the largest
source of error in diff
σ.
VI. FUTURE WORK
Future work includes repeating the above measurements for
thinner CCDs, 200
µ
m in particular, to verify the thickness
scaling of the lateral diffusion predicted in (5). We will also
measure smaller pixel sizes, in particular 10.5
µ
m, to verify
that the virtual knife edge technique is indeed independent of
pixel size. CCDs are in fabrication that can operate with a
150 V substrate bias. Again, this will provide more leverage to
validate the voltage scaling of (5).
We are presently using the apparatus described here to
measure lateral charge diffusion in other LBNL CCDs,
varying in thickness and pixel size. With improvements in
lamp stability and monitoring and eliminating the problem in
the y positioning system, we plan to make use of the small
projected beam profile to measure any intra-pixel variance
that might exist in these CCDs.
VII. CONCLUSIONS
We have successfully developed and applied a virtual knife-
edge technique for measuring the lateral charge diffusion in a
CCD. Using this technique, we measured the PSF of a
280
µ
m thick, back-illuminated p-channel n-type over-
depletable LBNL CCD. We demonstrated that the PSF width
for this CCD varies from 89.9±3.0
µ
m to 6.38
±
0.24
µ
m
as the substrate bias voltage increases from 6 V to 77 V.
Scaling according to (5), a 4
µ
m rms diffusion should be
achievable in a 200
µ
m thick device operated at 80 V.
VIII. ACKNOWLEDGEMENTS
We thank Steve Holland, Nick Palaio, and Guobin Wang of
LBNL for manufacturing and providing the CCDs studied
here. We also thank Steve Holland and Don Groom of LBNL
for discussions on the theoretical underpinnings of the
diffusion analysis.
IX. .REFERENCES
[1] S. E. Holland G. Goldhaber, D. E. Groom, W. W. Moses, C. R.
Pennypacker, S. Perlmutter, N. W. Wang, R. J. Stover, and M. Wei,, "A
200 $\times$ 200 CCD image sensor fabricated on high-resistivity silicon,"
in IEDM Technical Digest, pp. 911-914, 1996.
[2] S. E. Holland, N. W. Wang, and W. W. Moses, “Development of low noise,
back-side illuminated silicon photodiode arrays,” IEEE Trans. Nucl. Sci.,
vol. 44, no. 3, pp. 443-447, Jun. 1997.
[3] S. E. Holland, D. E. Groom, N. P. Palaio, R. J. Stover, and M. Wei, “Fully
Depleted, Back-Illuminated Charge-Coupled Devices Fabricated on High-
resistivity Silicon,” IEEE Trans. Electron Devices, vol. 50, pp. 225-238,
Jan. 2003.
[4] D. E. Groom, P. H. Eberhard, S. E. Holland, M. E. Levi, N. P. Palaio, S.
Perlmutter, R. J. Stover, and M. Wei., "Point-spread function in depleted
and partially depleted CCDs," in Proc. 4th ESO Workshop on Optical
Detectors for Astronomy, Garching, Germany, 13-16 Sep. 1999.
Fig. 1. At the top is shown a cross section of the CCD. A conventional three-phase, polysilicon gate structure is deposited on 200-300
µ
m thick n-type, high-resistivity
silicon. The channel implants are p-type. For back-illumination and backside electrical contact, a 2000 Å in situ poly-doped window is deposited. The depletion
voltage is applied to this contact. At the bottom, a MEDICI simulation of the electric field near the collection surface of the CCD is shown. The bias voltage is 40 V.
Three clock gates are shown near y=0 with the middle gate in collection phase. Moving away from the pixel region, positive y, the electric field is seen to be spatially
uniform and of approximately linear. This linear region extends to the backside of the CCD, leaving no field-free region.
Fig. 2: Schematic for virtual knife-edge technique.
Fig. 3: Top: Variation of total charge (normalized) in integration region versus scan position. The smooth curve shows a fit to an error function. Bottom: Derivative of
total charge (normalized) variation in integration region versus scan position. The smooth curve shows a fit to a gaussian. The total charge in the integration region is
normalized to the total charge read out on the CCD.
Fig. 4: Experimental setup used for lateral charge diffusion measurement.
Fig. 5: Variation of total charge collected on CCD versus scan position. The variation observed may be caused by a temporal fluctuation of the lamp intensity and/or
intra-pixel response variations.
Fig. 6: Charge profiles on CCD at substrate voltages of 5.8 V, 12.1 V, 61.5 V, and 76.8 V.
Fig. 7: Left: Variation of PSF )( diff
σ with substrate bias voltage )V( sub at 450 nm, 550 nm, and 650 nm in the x-(row) direction. Right: Variation of PSF
)( diff
σ with substrate bias voltage )V( sub at 650 nm in the x (row) and y (column) directions. The dashed curves indicate the theoretical fit based on the one-
dimensional analytical model discussed in [3]. The error bars in both plots include both statistical and systematic uncertainties.
Fig. 8: Variation of the charge fraction in the central pixel versus encoder position for adjacent pixels.
Fig. 9: Variation of fraction of charge in central pixel versus encoder position. Left is for a row scan; right is for a column scan. The deviation of the average position
from 15
µ
m can be attributed to position encoder calibrations. The distorted distribution for the column scan is under investigation.
Table I: Intrinsic beam width measurements.
Table II: Measurements of diff
σ at 450 nm.
Table III: Measurements of diff
σ at 550 nm.
Table IV: Measurements of diff
σ at 650 nm.
Table I: Intrinsic beam width measurements.
Wavelength (nm) σbeam (µm)
450 1.26 ± 0.10
550 1.19 ± 0.10
650 1.39 ± 0.10
Fig. 1. At the top is shown a cross section of the CCD. A conventional three-phase,
polysilicon gate structure is deposited on 200-300
µ
m thick n-type, high-resistivity silicon.
The channel implants are p-type. For back-illumination and backside electrical contact, a 2000
Å in situ poly-doped window is deposited. The depletion voltage is applied to this contact. At
the bottom, a MEDICI simulation of the electric field near the collection surface of the CCD
is shown. The bias voltage is 40 V. Three clock gates are shown near y=0 with the middle
gate in collection phase. Moving away from the pixel region, positive y, the electric field is
seen to be spatially uniform and of approximately linear. This linear region extends to the
backside of the CCD, leaving no field-free region.
Fig. 2: Schematic for virtual knife-edge technique.
Fig. 3: Top: Variation of total charge (normalized) in integration region versus scan position.
The smooth curve shows a fit to an error function. Bottom: Derivative of total charge
(normalized) variation in integration region versus scan position. The smooth curve shows a
fit to a gaussian. The total charge in the integration region is normalized to the total charge
read out on the CCD.
Fig. 4: Experimental setup used for lateral charge diffusion measurement.
Fig. 5: Variation of total charge collected on CCD versus scan position. The variation
observed may be caused by a temporal fluctuation of the lamp intensity and/or intra-pixel
response variations.
Fig. 6: Charge profiles on CCD at substrate voltages of 5.8 V, 12.1 V, 61.5 V, and 76.8 V.
Fig. 7: Left: Variation of PSF (σdiff) with substrate bias voltage (Vsub) at 450 nm, 550 nm, and
650 nm in the x-(row) direction. Right: Variation of PSF (σdiff) with substrate bias voltage
(Vsub) at 650 nm in the x (row) and y (column) directions. The dashed curves indicate the
theoretical fit based on the one-dimensional analytical model discussed in [3]. The error bars
in both plots include both statistical and systematic uncertainties.
Fig. 8: Variation of the charge fraction in the central pixel versus encoder position for
adjacent pixels.
Fig. 9: Variation of fraction of charge in central pixel versus encoder position. Left is for a
row scan; right is for a column scan. The deviation of the average position from 15 µm can be
attributed to position encoder calibrations. The distorted distribution for the column scan is
under investigation.
Table II: Measurements of σdiff at 450 nm.
σdiff (µm)
Vsub |x| scan |y| scan
5.9 90.8 ± 3.9 85.9 ± 3.4
7.5 75.3 ± 2.5 73.7 ± 2.5
10.1 54.4 ± 2.8 54.5 ± 2.6
12.1 39.5 ± 3.0 36.8 ± 1.6
16.0 17.7 ± 0.8 17.2 ± 1.0
21.0 13.0 ± 0.5 12.8 ± 0.8
31.8 10.1 ± 0.4 9.8 ± 0.6
44.8 8.4 ± 0.4 8.2 ± 0.5
61.5 7.0 ± 0.3 6.7 ± 0.5
74.9 6.4 ± 0.3 6.3 ± 0.4
Table III: Measurements of σdiff at 550 nm.
σdiff (µm)
Vsub |x| scan |y| scan
5.9 91.8 ± 3.1 90.1 ± 3.0
7.5 78.8 ± 2.7 76.8 ± 2.6
10.1 54.1± 3.0 54.5 ± 2.4
12.1 38.7 ± 3.0 36.2 ± 1.5
16.0 17.8 ± 0.9 17.0 ± 0.9
21.0 12.8 ± 0.5 12.3 ± 0.6
31.8 9.8 ± 0.5 9.5 ± 0.5
44.8 8.3 ± 0.3 8.0 ± 0.5
61.5 7.0 ± 0.3 6.8 ± 0.4
78.8 6.6 ± 0.3 6.2 ± 0.4
Table IV: Measurements of σdiff at 650 nm.
σdiff (µm)
Vsub |x| scan |y| scan
5.9 90.3 ± 3.0 86.6 ± 4.2
7.5 80.6 ± 2.7 79.4 ± 4.5
10.1 52.9 ± 2.5 52.4 ± 2.6
12.1 37.4 ± 3.0 37.5 ± 2.5
16.0 16.8 ± 0.6 16.1 ± 0.7
21.0 12.8 ± 0.6 12.5 ± 0.7
31.8 9.8 ± 0.5 9.4 ± 0.5
44.8 8.2 ± 0.5 8.0 ± 0.5
61.5 7.1 ± 0.3 6.8 ± 0.4
76.8 6.4 ± 0.3 6.1 ± 0.4
