Abstract

Initial measurements of the position sensitivity of a visible-light multi-anode microchannel array (MAMA) detector show that centroid calculations for image spots are accurate to better than 0.04 pixels even with sources that are essentially delta functions at the photocathode. Subpixel sensitivity variations of 10–15% are typically found for pixels in the array. Variations as large as 30% are possible in the worst conditions. These variations limit the photometric accuracy of the detector when very small scale features are observed. The photometric accuracy and the position sensitivity of the detector appear to be limited by cross-coupling effects within the anode array. Initial measurements with more recent designs of the detector show that most or all of this cross-coupling has been eliminated. We will report on the position sensitivity of the newer detectors when they become available for testing.

© 1989 Optical Society of America

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References

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  1. N. Bobroff, “Position Measurement with a Resolution and Noise-Limited Instrument,” Rev. Sci. Instrum. 57, 1152 (1986).
    [CrossRef]
  2. S. E. Bulau, “Simulations of Various Centroding Algorithms,” Proc. Soc. Photo-Opt. Instrum. Eng. 627, 680 (1986).
  3. G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, J. Stein, “On the Astrometric Detection of Neighboring Planetary Systems, II,” NASAConf.Publ.2124 (1980), pp. 77–118.
  4. G. Gatewood, J. Stein, C. Difatta, K. DeJonge, L. Breakiron, “A Preliminary Look at Astrometric Accuracy as a Function of Photon Counts,” Astron. J. 90, 2397 (1985).
    [CrossRef]
  5. C. KenKnight, “Limit Posed for Astrometry by Earth’s Atmosphere,” NASAConf.Publ.2124 (1980), pp. 55–60.
  6. J. G. Timothy, R. L. Bybee, “Photon-Counting Array Detectors for Space and Ground-Based Studies at Ultraviolet and Vacuum Ultraviolet (VUV) Wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 279, 129 (1981).
  7. W. E. Spicer, “The Production of Pairs in Semiconductors by Low Energy Electrons,” J. Phys. Chem. Solids 22, 365 (1961).
    [CrossRef]
  8. J. M. Grant, “Note on the Proximity Focusing of Electron Images,” Proc. IEEE 54, 801 (1966).
    [CrossRef]
  9. E. H. Eberhardt, “Image Transfer Properties of Proximity Focused Image Tubes,” Appl. Opt. 16, 2127 (1977).
    [CrossRef] [PubMed]
  10. J. G. Timothy, “Imaging at Soft X-Ray Wavelengths with High-Gain Microchannel Plate Detector Systems,” Proc. Soc. Photo-Opt. Instrum. Eng. 691, 35 (1986).
  11. X. X. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  12. S. Brandt, Statistical and Computational Methods in Data Analysis (North-Holland, Amsterdam, 1983).
  13. J. G. Timothy, “Curved-Channel Microchannel Array Plates,” Rev. Sci. Instrum. 52, 1131 (1981).
    [CrossRef]

1986 (3)

N. Bobroff, “Position Measurement with a Resolution and Noise-Limited Instrument,” Rev. Sci. Instrum. 57, 1152 (1986).
[CrossRef]

S. E. Bulau, “Simulations of Various Centroding Algorithms,” Proc. Soc. Photo-Opt. Instrum. Eng. 627, 680 (1986).

J. G. Timothy, “Imaging at Soft X-Ray Wavelengths with High-Gain Microchannel Plate Detector Systems,” Proc. Soc. Photo-Opt. Instrum. Eng. 691, 35 (1986).

1985 (1)

G. Gatewood, J. Stein, C. Difatta, K. DeJonge, L. Breakiron, “A Preliminary Look at Astrometric Accuracy as a Function of Photon Counts,” Astron. J. 90, 2397 (1985).
[CrossRef]

1981 (2)

J. G. Timothy, R. L. Bybee, “Photon-Counting Array Detectors for Space and Ground-Based Studies at Ultraviolet and Vacuum Ultraviolet (VUV) Wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 279, 129 (1981).

J. G. Timothy, “Curved-Channel Microchannel Array Plates,” Rev. Sci. Instrum. 52, 1131 (1981).
[CrossRef]

1977 (1)

1966 (1)

J. M. Grant, “Note on the Proximity Focusing of Electron Images,” Proc. IEEE 54, 801 (1966).
[CrossRef]

1961 (1)

W. E. Spicer, “The Production of Pairs in Semiconductors by Low Energy Electrons,” J. Phys. Chem. Solids 22, 365 (1961).
[CrossRef]

Bevington, X. X.

X. X. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Bobroff, N.

N. Bobroff, “Position Measurement with a Resolution and Noise-Limited Instrument,” Rev. Sci. Instrum. 57, 1152 (1986).
[CrossRef]

Brandt, S.

S. Brandt, Statistical and Computational Methods in Data Analysis (North-Holland, Amsterdam, 1983).

Breakiron, L.

G. Gatewood, J. Stein, C. Difatta, K. DeJonge, L. Breakiron, “A Preliminary Look at Astrometric Accuracy as a Function of Photon Counts,” Astron. J. 90, 2397 (1985).
[CrossRef]

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, J. Stein, “On the Astrometric Detection of Neighboring Planetary Systems, II,” NASAConf.Publ.2124 (1980), pp. 77–118.

Bulau, S. E.

S. E. Bulau, “Simulations of Various Centroding Algorithms,” Proc. Soc. Photo-Opt. Instrum. Eng. 627, 680 (1986).

Bybee, R. L.

J. G. Timothy, R. L. Bybee, “Photon-Counting Array Detectors for Space and Ground-Based Studies at Ultraviolet and Vacuum Ultraviolet (VUV) Wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 279, 129 (1981).

DeJonge, K.

G. Gatewood, J. Stein, C. Difatta, K. DeJonge, L. Breakiron, “A Preliminary Look at Astrometric Accuracy as a Function of Photon Counts,” Astron. J. 90, 2397 (1985).
[CrossRef]

Difatta, C.

G. Gatewood, J. Stein, C. Difatta, K. DeJonge, L. Breakiron, “A Preliminary Look at Astrometric Accuracy as a Function of Photon Counts,” Astron. J. 90, 2397 (1985).
[CrossRef]

Eberhardt, E. H.

Gatewood, G.

G. Gatewood, J. Stein, C. Difatta, K. DeJonge, L. Breakiron, “A Preliminary Look at Astrometric Accuracy as a Function of Photon Counts,” Astron. J. 90, 2397 (1985).
[CrossRef]

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, J. Stein, “On the Astrometric Detection of Neighboring Planetary Systems, II,” NASAConf.Publ.2124 (1980), pp. 77–118.

Goebel, R.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, J. Stein, “On the Astrometric Detection of Neighboring Planetary Systems, II,” NASAConf.Publ.2124 (1980), pp. 77–118.

Grant, J. M.

J. M. Grant, “Note on the Proximity Focusing of Electron Images,” Proc. IEEE 54, 801 (1966).
[CrossRef]

KenKnight, C.

C. KenKnight, “Limit Posed for Astrometry by Earth’s Atmosphere,” NASAConf.Publ.2124 (1980), pp. 55–60.

Kipp, S.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, J. Stein, “On the Astrometric Detection of Neighboring Planetary Systems, II,” NASAConf.Publ.2124 (1980), pp. 77–118.

Russel, J.

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, J. Stein, “On the Astrometric Detection of Neighboring Planetary Systems, II,” NASAConf.Publ.2124 (1980), pp. 77–118.

Spicer, W. E.

W. E. Spicer, “The Production of Pairs in Semiconductors by Low Energy Electrons,” J. Phys. Chem. Solids 22, 365 (1961).
[CrossRef]

Stein, J.

G. Gatewood, J. Stein, C. Difatta, K. DeJonge, L. Breakiron, “A Preliminary Look at Astrometric Accuracy as a Function of Photon Counts,” Astron. J. 90, 2397 (1985).
[CrossRef]

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, J. Stein, “On the Astrometric Detection of Neighboring Planetary Systems, II,” NASAConf.Publ.2124 (1980), pp. 77–118.

Timothy, J. G.

J. G. Timothy, “Imaging at Soft X-Ray Wavelengths with High-Gain Microchannel Plate Detector Systems,” Proc. Soc. Photo-Opt. Instrum. Eng. 691, 35 (1986).

J. G. Timothy, R. L. Bybee, “Photon-Counting Array Detectors for Space and Ground-Based Studies at Ultraviolet and Vacuum Ultraviolet (VUV) Wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 279, 129 (1981).

J. G. Timothy, “Curved-Channel Microchannel Array Plates,” Rev. Sci. Instrum. 52, 1131 (1981).
[CrossRef]

Appl. Opt. (1)

Astron. J. (1)

G. Gatewood, J. Stein, C. Difatta, K. DeJonge, L. Breakiron, “A Preliminary Look at Astrometric Accuracy as a Function of Photon Counts,” Astron. J. 90, 2397 (1985).
[CrossRef]

J. Phys. Chem. Solids (1)

W. E. Spicer, “The Production of Pairs in Semiconductors by Low Energy Electrons,” J. Phys. Chem. Solids 22, 365 (1961).
[CrossRef]

Proc. IEEE (1)

J. M. Grant, “Note on the Proximity Focusing of Electron Images,” Proc. IEEE 54, 801 (1966).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

J. G. Timothy, R. L. Bybee, “Photon-Counting Array Detectors for Space and Ground-Based Studies at Ultraviolet and Vacuum Ultraviolet (VUV) Wavelengths,” Proc. Soc. Photo-Opt. Instrum. Eng. 279, 129 (1981).

S. E. Bulau, “Simulations of Various Centroding Algorithms,” Proc. Soc. Photo-Opt. Instrum. Eng. 627, 680 (1986).

J. G. Timothy, “Imaging at Soft X-Ray Wavelengths with High-Gain Microchannel Plate Detector Systems,” Proc. Soc. Photo-Opt. Instrum. Eng. 691, 35 (1986).

Rev. Sci. Instrum. (2)

J. G. Timothy, “Curved-Channel Microchannel Array Plates,” Rev. Sci. Instrum. 52, 1131 (1981).
[CrossRef]

N. Bobroff, “Position Measurement with a Resolution and Noise-Limited Instrument,” Rev. Sci. Instrum. 57, 1152 (1986).
[CrossRef]

Other (4)

G. Gatewood, L. Breakiron, R. Goebel, S. Kipp, J. Russel, J. Stein, “On the Astrometric Detection of Neighboring Planetary Systems, II,” NASAConf.Publ.2124 (1980), pp. 77–118.

C. KenKnight, “Limit Posed for Astrometry by Earth’s Atmosphere,” NASAConf.Publ.2124 (1980), pp. 55–60.

X. X. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

S. Brandt, Statistical and Computational Methods in Data Analysis (North-Holland, Amsterdam, 1983).

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Figures (17)

Fig. 1
Fig. 1

(a) Schematic of a typical MAMA detector for use at EUV and soft x-ray wavelengths. (b) Schematic of a visible-light MAMA detector with a semitransparent, proximity focused photocathode.

Fig. 2
Fig. 2

Microphotograph of the pores in a microchannel plate. The pore diameters are 12μm on 15-μm centers.

Fig. 3
Fig. 3

Ratio of two flat fields taken 58 days apart. The flat-field exposures are reproducible to within the statistical errors of the exposures. For each flat field n = 800 counts.

Fig. 4
Fig. 4

Simplified layout of one level of the anode array. The spots denote the size of charge clouds from the MCP. Coarse electrodes are at the top of the diagram and fine electrodes are at the bottom.

Fig. 5
Fig. 5

Theoretical calculations of the sampling errors as a function of input spot width. Gaussian spots are assumed. The FWHM spot widths are given in units of a pixel. A uniform pixel response is assumed.

Fig. 6
Fig. 6

Effects of a nonuniform pixel response on the sampling errors. (a) Various profiles of g(x) assumed. The peak sensitivity of profiles 2 and 3 have been decreased from 1 to more clearly illustrate their shapes. (b) Sampling errors calculated by assuming the pixel response curves shown in (a) and a Gaussian input spot of 1-pixel FWHM.

Fig. 7
Fig. 7

Schematic of the experimental setup.

Fig. 8
Fig. 8

Micrometer measurements of errors in the stepper motor motions. The stepper motor is geared to 1-μm steps on the detector with 200 steps/revolution. The dashed line shows the corrections for the gear motion errors that were applied to the position measurements.

Fig. 9
Fig. 9

Results of a knife-edge test with a pinhole of 50-μm diameter. (a) The x profile of a spot is shown 100 steps from best focus. The dashed line shows a Gaussian profile with 3.3-μm FWHM. (b) The asymmetric profile of an out-of-focus spot is shown. The doughnut structure of the beam is clearly visible. Its FWHM is 29 μm.

Fig. 10
Fig. 10

Our focus curve. The plot shows the spot diameter (FWHM) as determined from knife-edge measurements as a function of distance from best focus.

Fig. 11
Fig. 11

(a) Plot of known position vs derived centroid position for a spot of 3.5-μm diameter. A linear least-squares fit is shown superimposed on the data. (b) The data from (a) are shown with the linear trend subtracted. The bar in the corner indicates the magnitude of the Poisson errors for these data.

Fig. 12
Fig. 12

Solid line shows the power spectrum of Fig. 11(b). The spatial frequency scale is normalized to the Nyquist frequency of the measurements (fNyquist = ⅙ cycle μm1). The dashed curves show the power spectra of synthetic residual curves which were constructed by adding Poisson noise (σ = 0.015 pixels) to sampling errors with amplitudes of 0.04 pixels (long dashed curve) and 0.02 pixels (short dashed curve). The absolute spatial frequencies of the prominent peaks in the spectra of the measured residuals are labeled.

Fig. 13
Fig. 13

(a) Centroid residuals are shown for a spot size of 40-μm diameter. The format of the plot is identical to Fig. 11. (b) The power spectrum of the residuals shown in (a) is plotted.

Fig. 14
Fig. 14

A 50- × 50-μm map of the subpixel variations in the detector’s detective quantum efficiency (DQE). Light lines show contours of the detector DQE. Heavy lines show contours of the pixel centers and boundaries as determined by centroid measurements. The DQE contours are labeled in percentage of the peak efficiency seen near the pixel center. The coordinates of the pixel boundaries are labeled at the sides of the figure.

Fig. 15
Fig. 15

(a) Pixel response curve derived from Fig. 14. The dashed curves show the assumed contributions of twofold and threefold events to the total response curve which is shown by the solid line. (b) A synthetic DQE map derived from assuming an effective input spot size of 18-μm FWHM and the response curve shown in (a).

Fig. 16
Fig. 16

Photometric response of the detector when spots are moved across the detector. The small and large spots were 3.5- and 40-μm FWHM, respectively. The decreasing counts toward large source positions were due to vignetting in the microscopic objective.

Fig. 17
Fig. 17

Comparison of the flat fields from MAMA detectors employing course–fine and fine–fine anode arrays. The pixel-to-pixel variations in the coarse–fine detector are dominated by cross-coupling effects while the data from the fine–fine detector are dominated by the photon shot noise.

Equations (27)

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r = 2 D V e / V d ,
x c = i j N x j n i j i j N n i j and y c = i j N y j n i j i j N n i j ,
s x 2 x 2 = s u 2 u 2 + s υ 2 υ 2 2 s u υ u υ ,
s u 2 = ( u u ) 2 = u 2 u 2 ,
s u υ = ( u u ) ( υ υ ) = u υ u υ ,
u = i j N x j n i j   and υ = i j N n i j   .
s u 2 = i j N s i j 2 x j 2 + i j     k l N s i j k l x j x k ,
s υ 2 = i j N s i j 2 + i j     k l N s i j k l ,
s u υ = i j N s i j 2 x j + i j     k l N s i j k l x j ,
n i j = n f ( n i j ) o ( n i j ) f ,
s i j 2 = n i j + σ r 2 .
s i j 2 = n i j ( 1 + n i j n f )  .
s x 2 = 1 i j N n i j ( σ x 2 + σ r 2 f ) ,
σ x = ( x 2 x 2 ) 1 / 2 ,
x = i j N n i j x j i j N n i j ,
x 2 = i j N n i j x j 2 i j N n i j ,
f = i j N x j 2 + N x 2 2 x i j N x j i j N n i j .
n i j a = i j N n i j N ,
s x 2 = σ x 2 i j N n i j ( 1 + σ r 2 a )   .
s x 2 = 1 i j N n i j [ σ x 2 + 1 n f ( n x 2 + n x 2 2 x n x ) ]   ,
n x 2 = i j N n i j 2 x j 2 i j N n i j .
s x 2 = σ x 2 i j N n i j ( 1 + a n f )   ,
x c = x f ( x ) d x f ( x ) d x ,
x i = ( x i + 1 + x i 2 )   .
x d = i x i x i x i + 1 g ( x ) f ( x ) d x i x i x i + 1 g ( x ) f ( x ) d x .
Δ x x c x d .
Δ x = i x i x i + 1 f ( x ) ( x x i ) d x f ( x ) d x .

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