Pushing the Limits of Spatial Resolution with pnCCDs

Pushing the Limits of Spatial Resolution with pnCCDs Peter Holl, Robert Hartmann, Sebastian Ihle, David Kalok, Lothar Strüder PNSensor GmbH, München

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Outline t Introduction ● pnCCD Properties: the Color X-ray Camera ● “Spatial Resolution” t Monte Carlo Simulator for Pixel Detectors ● From Photons to Signals ● Improving Centroiding and Pixel Selection ● Results t Measurements at BESSY II (MAXYMUS) ● Setup of the Scanning X-ray Microscope ● Experimental Results vs. Simulation t Conclusions and Outlook

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The Color X-ray Camera Specifications Parameter

pnCCD Properties

Physical pixel size

48 µm × 48 µm [ × 450 µm Depth]

Image area pixels

264 × 264 (70 Kilopixels)

Number of subpixels

3200 × 3200 (10 Megapixels)

Image area

12.7 mm × 12.7 mm (A = 161 mm2)

Full frame rate

Up to 1,000 Hz

Window mode rate

Up to 20,000 Hz

Binning mode

Up to 8-fold binning

Windowing mode

24 × 264 pixels (smallest window)

Pixel readout rate

Up to 70 Megapixels/s

Externally triggerable

yes

Readout noise (RMS)

ENC < 3 e-/pixel @ 400 Hz, < 4 e- @ 1,000 Hz

Energy resolution

140 eV FWHM @ Mn-K "

Sensor spatial resolution

R[σ] < 1 µm for 6 keV X-rays

Charge handling capacity

Up to 400,000 signal electrons per pixel

Radiation hardness

up to 1014 photons/cm2 @ 10 keV

Back illuminated, fully depleted pnCCD, high-speed and low noise readout, high quantum efficiency, flexible operation, entrance windows variants for X-rays, optical photons, and electrons.

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Introduction | Image Resolution Many Photons/Pixel ➠ Resolution ≈ 2 x Pixel Size (Nyquist Criterion, Shannon’s Sampling Theorem) Example: experiment at the Linac Coherent Light Source (LCLS) with the CAMP Chamber diffraction pattern of a single mimivirus taken with a 1 Megapixel pnCCD camera up to 300,000 electrons ≈ 570 X-ray photons with 1.8 keV per 75µm x 75µm pixel

➠

Image reconstruction (Hawk software*)

➠

*Reference:

Single mimivirus particles intercepted and imaged with an X-ray laser; Nature 470, 78–81 (03 February 2011) doi:10.1038/nature09748

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Introduction | Spatial Resolution II Single Photon/Multi Pixel events (pnCCDs, DEPFeT pixels, etc.):

14% 60% ×

10% 16%

48µm

For Single Photon Measurements Spatial Resolution can be defined as RMSD 𝐑[𝝈] =

𝟏 ,( 𝒙𝒎𝒆𝒂𝒔 − 𝒙 𝒏

𝟐

+ 𝒚𝒎𝒆𝒂𝒔 − 𝒚 𝟐)

𝐑[𝝈] ≪ pixel size, e.g. 𝐑[𝝈] ≈ 1 µm with 48 µm x 48 µm pixels (6 keV photons) iWoRiD, Krakow, July 2017

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Charge Collection in Pixel Structure 𝑧ℎ𝑖𝑡 𝑦ℎ𝑖𝑡

Charge cloud size 𝛔 depends on: Energy ➠ electrostatic repulsion zhit ➠ Collection time Temperature, mobility, collecting field

𝑥ℎ𝑖𝑡 ×

Interaction point

@B

F

E ? 1 = 𝑒 𝜋𝛔

@B

@?@ABC 𝛔D

D

IB

EF

dx =

? I?IABC 𝑒 𝛔D

D

dy

IB

Can also be interpreted as the probability for an electron, generated at (𝒙𝒉𝒊𝒕, 𝒚𝒉𝒊𝒕) to be collected in the pixel ([𝒙𝒊, 𝒙𝒊+1], [𝒚𝒊, 𝒚𝒊+1])

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Monte Carlo Simulation 1. Incoming X-rays: ● Energy (1320 eV) ● Incident Position x,y & angle (line and random flat field, vertical) ● Rate: photons / frame (n/a) 2. Photoelectric Interaction: ● Position x,y,z: random from angle & absorption length (5.7 µm) ●

Number of signal electrons: random from Fano statistics (≅ 358 ±7)

● Escape, Compton scattering, dead layer, etc. (n/a) 3. Charge Collection and Signal: ● Drift time into pixel: tdrift =f(z, E-Field, T) (≲ 11.7 ns) ● Width of charge cloud: σ = f(tdrift, Nelectrons, T) (≲ 12.4 µm) ● Signal per pixel: random from x,y,σ and geometry (48 µm x 48 µm) ● Noise added to pixel: random from ENC (3.5 e- or 5.5 e-) 4. Result: “frames file” output; Inline event analysis (playground for tests) with statistic data output iWoRiD, Krakow, July 2017

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Position Reconstruction | Gauss-Correction X-rays incident along diagonal lines Lookup table applied for x and y coordinates

48

40

32

24

➠

16

8

0 0

8

16

24

32

40

48

➠

Positions after Gauss-Correction

Positions reconstructed with Center of Gravity Lookup table to correct for the Gaussian shape of the charge cloud is calculated from pixel geometry (48 µm x 48µm), and from the average size of the charge cloud (𝛔 = 12.4 µm); 𝛔 depends on X-ray energy (absorption length and electrostatic repulsion), temperature, depletion voltage, detector thickness, depth of transfer channel.

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Signal Selection | Threshold Method 4 pixels 3 pixels 48 µm

2 pixels

> 4σ ? > 4σ ? > 4σ ? > 4σ ? max.

𝟏 𝛔 ≈ 3.5 e- ENC

> 4σ ?

1 pixel

> 4σ ?

Input: Flat field with 𝟏𝟎𝟎×𝟏𝟎𝟔 photons ∼43,000 photons per 1 µm x 1 µm square Output: ➠

> 4σ ? > 4σ ?

The Dilemma: With no threshold • almost uniform distribution • but more noise ➠ worse resolution With threshold (e.g. 1 𝛔𝐄𝐍𝐂) • still far from uniform distribution • O.K. resolution Can we do better? iWoRiD, Krakow, July 2017

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Signal Selection | Map Method Use a predefined lookup-map with a low threshold (e.g. 2 electrons), calculated from the theoretical distribution (without noise) to decide which pixels to use for the evaluation:

yes

yes

yes

no

no

no

no

no

no

no

no

yes!

yes!

yes!

no

yes

yes!

yes!

no

yes!

no yes!

yes!

no

Analysis must be done recursively: • First centroiding with threshold method (or no threshold) • Second centroiding using map • Repeat? Maybe once. Still fast since no complex arithmetic involved. Boolean lookup-map is calculated once per energy.

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Signal Selection | Map vs. Threshold 6 pixels

51,000/µm2

5 pixels 4 pixel 43,400/µm2

Mapped ➠

➠

35,000/µm2

4 pixels 3 pixels

1.4x106/µm2

2 pixels 1 pixel

900,000/µm2

500,000/µm2

4 𝛔𝐄𝐍𝐂 thresh. ➠ 0

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➠

Signal Selection | Methods Compared Simulation parameters: 48 µm pnCCD, 450 µm substrate, -30˚C, VD = -120 V, 1320 eV X-rays flat field, charge cloud size = 12.4 µm

[µm]

rms of 1D spatial resolution within pixel averaged over other dimension

3

3x3 (no Threshold)

4 𝛔 Threshold 2.5

1 𝛔 (3.5 e-) Threshold

2

1.5

Map Method 1

0.5

0 0

8

16

24 3x3

4σ thresh

32 1σ thresh

mapped

40

48

x-position within pixel [µm]

2D spatial resolution within pixel for Map Method 𝐑[𝝈] = 2 µm

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Simulation Results | σpos vs. Energy Position resolution (rms), 48µm pnCCD, T = -30C, VD = -140V, ENC = 3.5e-

[µm] 16

charge cloud diameter (σ) 14

12

10

8

1320 eV 6

σpos (all events)

4

2

0 1000

σpos (without singles) 3000

5000

7000 σ (no singles)

9000 σ (all)

11000

13000

15000

[eV]

CC Size

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Setup of an X-ray Microscope longer focal length removed replaced by Detector (pnCCD)

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Measurement Setup at BESSY II (MAXYMUS) 1st

order spot

Zone plate

Beam path to 1st order spot

Photon positions 24 23.5

Beam path to 0th order illumination

23 22.5

Y direction

22

X-ray beam with 1320 eV; ~1200 photons/s

21.5 21 20.5 20 19.5 19 128 128.5 129 129.5 130 130.5 131 131.5 132

0th order illumination

Fresnel Zone Plate Properties*) Focal length

8.7 cm @ 1200 eV

Focal spot size

0.7 µm (ideal) 1 µm – 3 µm (realistic)

Diameter

180 µm

Zone width

0.5 µm

Our thanks to Markus Weigand and Michael Bechtel from the MPIIS / MAXYMUS (MAgnetic X-raY Microscope with UHV Spectroscopy) team. *)

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Measurement | Position Scan Measured position resolution XY-scan positions • • • • •

Y direction in µ m

80 70

154 positions scanned Δx = 3 µm, Δy = 10 µm dwell time 85 s / position ~ 100,000 photons / position (initially) scanned area 1.25 x 1.3 pixels

60

(Parameters chosen to finish the experiment in the limited beamtime!)

50

pixel boundaries

40

scanned locations (reconstructed) with error bars indicating the spatial resolution

30 20 10 30

40

50

60

70

80 90 X direction in µ m

pixel boundaries iWoRiD, Krakow, July 2017

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Measurement Results | Spectrum 100000





FWHM 127 eV (53.9 eV r.m.s.) → ~𝟏𝟑. 𝟑 e− ENC/event ( ≈ 6 e− ENC/pixel) 10000

Pile-up peaks 1000

100

10

1 0

500

1000

1500

1320 eV

2000 3x3sum

2500 E-window

3000

3500

4000

4500

5000 [eV]

XY-window

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Measurement Results | Position Histogram

3 x 3 pixels shown

Overlay of all events, peak positions shifted to [120,120] Position window to reject 0-order background

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Measurement Results | Position precision 4

MC simulation parameters: 5.5 e- ENC 1.1 µm “spot noise”

3.5

3

2.5

2

1.5

1

0.5

0

[µm] 0

4

8

12 simulation

16

20

24

28

simulation !x(thresh 1!) x-position within pixel !x(map) !x(map) !x(3x3)

!x(map)

32 3x3

36

40

44

48

1-sigma

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Conclusions and Outlook § Using Monte Carlo simulations, we have developed the new “map method” for determining the interaction point of a single X-ray photon with very high precision. 𝐑[𝛔] ≲ 𝟐 µm between 1.3 keV and 11 keV with 48 µm x 48 µm pixels, 70k (264 x 264) px image ➠ 10M (3200 x 3200) px image, High-speed readout and spectroscopic performance are not affected, Reconstruction method uses look-up tables ➠ fast! § The simulations correspond very well with measurements from an X-ray microscope. Optimal method for simulated data ➠ optimal for experimental data, Spatial resolution 𝐑[𝛔] ≈ 2.5 µm at 1320 eV (non optimized setup) § More measurements are planned over a wider energy range, and to extend the reconstruction method to polychromatic X-ray exposures. Related Paper: S. Ihle, P. Holl et al., Direct measurement of the position accuracy for low energy X-ray photons with a pnCCD Journal of Instrumentation, Volume 12, February 2017; DOI:10.1088/1748-0221/12/02/P02005

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