Photodetection in Flow Cytometry - Hamamatsu Photonicshub.hamamatsu.com/sp/hc/resources/FC_Webinar.pdfSlide # 2 Outline 9/24/2019 Photodetection in Flow Cytometry 1. Introduction to

Slide # 1

Photodetection in Flow Cytometry

Slawomir PiatekNJIT/HamamatsuCopyright 2019 Hamamatsu

Slide # 2

Outline

9/24/2019 Photodetection in Flow Cytometry

1. Introduction to flow cytometry

b. Modes of light-cell interactions and signal formationa. Basic setup

c. Forward- and side-scatter configurationsc. Data acquisition and data display

2. Introduction to photodetectorsa. Structure and operationb. Opto-electronic characteristics

Slide # 3

Outline


3. Photodetection

a. Noise and signal-to-noise ratiob. Linearity and dynamic range

4. Summary and conclusion

c. Impact on scatter plots

Slide # 4

1. Introduction to flow cytometry


Slide # 5

Flow Cytometer consists of three components:

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Fluidics

Optics

ElectronicsPhotodetectors bridge these two components


Slide # 6

Fluidics – sample injection

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Interrogation oranalysis point

~100 μm~20 μm

• Hydrodynamic focusing creates a narrow flow, known as the core, where the cells arrange in a one-by-one file.

• The diameter of the core depends on the pressure difference between the sheath fluid and the core fluid.

• Only one cell at the time should be passing through the interrogation point.

• Sampling rate ~ 1,000 – 100,000 s-1


Slide # 7

Optics

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FD

SCD

FSD

Laser 1

Lase

r 2Data collection & analysis

Beam mixer

DM

DM

Flow

Legend:FSD – forward-scatter detectorSCD – side-scatter detector

FD – fluorescence detectorDM – dichroic mirror

Fluorescence-tagged cell


Slide # 8

Interrogation point

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Beam profile (typically Gaussian)before cylindrical lens (not to scale)

Beam profile at the interrogationpoint (not to scale). The long axis is perpendicular to the flow.

~100 μm~20 μm

interrogation point

cylindrical lens


Slide # 9

Light sources

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• Solid-state lasers are the most common illuminators in modern flow cytometers.

• They are compact, light weights, and can provide up to 150 mW of output power.

• Typical wavelengths [in nm]: 488, 505, 514, 532, 552, 561, 594


Slide # 10

Interaction of light with the cell: light signal generation

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reflection

refraction

Diffraction/scattering

fluorescence

absorption

cell


Slide # 11

Spurious light


𝑛𝑛1 𝑛𝑛2

Spurious light can be due to:

Impurities

Index of refraction differences

Flow turbulence

Slide # 12

Light signal formation

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20 μm

100 μm

10-μm cell

• For reasonable assumption, a 10 − 𝜇𝜇m cell will scatter about 5×1012 photons at the interrogation rate of 1,000 cells per second.


Slide # 13

Anatomy of a light signal

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𝜏𝜏

Pulse of light lens

𝜏𝜏Po

wer

time

Pulse duration

Peak power

Area of the pulse = total energy in the pulse


Slide # 14

Anatomy of a light signal


Approximating the pulse with a triangle, the peak power is related to the number of photon in the pulse as by:

𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 =2𝑁𝑁𝑁𝑁𝑁𝜏𝜏𝜏𝜏

For 𝜏𝜏 = 10 𝜇𝜇𝑠𝑠 and 𝜏𝜏 = 488 nm

𝑁𝑁 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 [W]

10

100

1,000

10,000

100,000

7.7 � 10−13

7.7 � 10−12

7.7 � 10−11

7.7 � 10−10

7.7 � 10−9

Slide # 15

Forward scatter

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Iris

Lens

Beam blocker

Flow cell

Photodetectortypically a photodiode

Filterλcenter = λlaser

1. The forward scatter signal is primarily determined by the size of the interrogated cell.

2. The peak forward scatter power at λ = 488 nm using 2-μm microspheres and 20-mW laser is about 4 μW.

side view


Slide # 16

Side scatter

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1. Light is a mixture of scattered laser light and fluorescence

2. Light level much lower than in the forward scatter

4. Need to use photodetectors with with intrinsic gain

3. Multiple fluorescence wavelengths can be present


Slide # 17

Side scatter optical setup

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APD/PMT/SiPM

Data processing

illuminating beam flow cell/interrogation point

collector and collimator

dich

roic

mirr

ors


Slide # 18

The role of the photodetector

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time

light

leve

l

time

photodetector electronics

voltage

• A photodetector + electronics convert the input light signal (a pulse) into electrical pulse (voltage as a function of time).

to A/D converter


Slide # 19

Current-to-voltage conversion

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PD R

i

Resistive termination

PD R

i−

+

RF

Transimpedance amplifier (pre-amplifier)

+ Simple circuit and inexpensive

+ Well-behaved frequency response

+ Well-understood noise (Johnson)

− Loads the PD, can lead to non-linearity

+ Virtual ground, no loading of the PD− Complex noise and frequency response− Needs biasing


𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 = 𝑖𝑖𝑖𝑖𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜 = −𝑖𝑖𝑖𝑖𝐹𝐹

virtual ground!

Slide # 20

Detection and data processing

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-

+

Vo

R

PD

Pre-amplifier

electronicsto measurepeak, area,or FWHM

A/D


Slide # 21

Flow Cytometer: what is measured?

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time

FWHM

Area

Peak

Out

put v

olta

ge fr

om p

ream

plifi

er

• The front end electronics can be set up to measure the peak value of the pulse, its FWHM, and/or area under the curve. These different measurements provide specific information about the cell.


Slide # 22

Scatter plots

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Forward-scatter signal

Side

-sca

tter s

igna

l

Fluorescence ch. 1Fl

uore

scen

ce c

h. 2


Scatter plots are ubiquitous to flow cytometry

Slide # 23

Histograms

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No.

of c

ells

(eve

nts)

Signal, e.g. side scatter


Histograms of a given measured quantity are also common

Slide # 24

2. Introduction to photodetectors

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photomultiplier tube

photodiode

avalanche photodiode

silicon photomultiplier


Slide # 25

Photomultiplier tube

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R1 R2 R3 R4 R5 R6 R7

C1 C2 C3

K P

D1 D2 D3 D4 D5 D6

V ~ 1000 VTypical voltage divider

Lighte−

Rf

VoutIPIK

Intrinsic gain of a PMT is about 105 - 107


Slide # 26

Solid-state photodetectors

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Si PIN photodiode Si APD SiPM

p

i

n

𝑉𝑉𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵

𝑖𝑖 𝑉𝑉𝑜𝑜𝑜𝑜𝑜𝑜

hν

p

n


hν

Gain =1 Gain up to ~100


hν hν

Gain ~106


𝑉𝑉𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 𝑉𝑉𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵

Slide # 27

Desired characteristics of photodetectors: photosensitivity

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Can we detect the “red” pulse?

PD E

• A photodetector’s photosensitivity depends on its quantum efficiency (function of wavelength) and intrinsic gain.


light

Slide # 28

Important points


1. Whether a light pulse is detected (that is, it has provided usefulscientific information), depends not only on the characteristics of thephotodetector but also on the characteristics of the front-endelectronics.

2. Without the front-end electronics, the photodetector is useless.

Slide # 29

Photosensitivity


wavelength

Qua

ntum

effi

cien

cy

wavelength

Spec

tral s

ensi

tivity

For a given wavelength, quantum efficiency, 𝜂𝜂, and spectral sensitivity, 𝑆𝑆𝜆𝜆, are related.

𝜂𝜂 =1240 � 𝑆𝑆𝜆𝜆𝜏𝜏 𝑛𝑛𝑛𝑛

Slide # 30

Photosensitivity: output current

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𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚𝜂𝜂𝜏𝜏 𝑛𝑛𝑛𝑛

1240𝜇𝜇 = 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚𝑆𝑆𝜆𝜆𝜇𝜇

PD

𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚

𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚 - Peak input light power

𝐼𝐼𝑚𝑚𝑚𝑚𝑚𝑚 - Peak output current

𝜂𝜂 - Quantum efficiency

light current

𝜏𝜏 - Wavelength (in nm)

𝜇𝜇 – Gain of the photodetector

𝑆𝑆𝜆𝜆 – Spectral sensitivity


Slide # 31

Closer look at the intrinsic gain

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PDOne photon

𝜇𝜇 electrons

R

Vout

PDOne photon

Oneelectron

R

Vout𝜇𝜇

Photodetector with gain 𝜇𝜇

=v/v

𝑆𝑆𝑁𝑁

𝑆𝑆𝑁𝑁


Slide # 32

Dark current

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1. Photodetector’s dark current results in the output signal offset from zero.

PD E

2. The variation around the mean is noise.

3. The magnitude of dark current depends on the photodetector’s bias voltage and temperature.


Slide # 33

Bandwidth

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Is there output signal pileup?Is a pulse structure resolved?

PD E

1. Insufficient bandwidth degrades signal fidelity. At high counting rates this may lead to signal pileup.

2. Detection bandwidth is determined by the photodetector and front-end electronics.


Slide # 34

Fourier representation and detection bandwidth

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time frequency

𝑃𝑃 𝜔𝜔

time

Arb.

frequency

𝑃𝑃 𝜔𝜔

↔

↔

timefrequency

𝑃𝑃 𝜔𝜔↔

Arb.

Arb. ”white” noise


Slide # 35

Detection bandwidth

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PD

RIntensity-modulated light input; 𝜔𝜔 modulation frequency

𝑉𝑉𝜔𝜔

𝑉𝑉 0

𝜔𝜔

12

Bandwidth

𝑉𝑉𝜔𝜔

• Both the photodetector and front-end electronics determine detection bandwidth.


Slide # 36

How much bandwidth do I need?

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time

|f(t)|2

|fmax|2

½|fmax|2 δt

|f(ω)|2

|fmax|2

½|fmax|2δω

0

~

~

~

Fourier transform

• The spectral composition depends on the pulse shape and its duration.

ω

For Gaussian pulse:

δt.δω = 4.log(2) ≈ 2.7726 (time-bandwidth product)


Slide # 37

Bandwidth

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• Too much bandwidth adds noise (indicated by thicker line)

PD E


Slide # 38

Bandwidth


100 kHz bandwidth 10 MHz bandwidth

Slide # 39

3. Photodetection


Slide # 40

Detection signal-to-noise ratio

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R

light

PD

To signal processing

𝑆𝑆𝑁𝑁


Slide # 41

Sources of noise: gain variation

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�𝑆𝑆𝑁𝑁 𝑖𝑖𝑖𝑖

�𝑆𝑆𝑁𝑁 𝑜𝑜𝑜𝑜𝑜𝑜

Gain section of a photodetector

F=�𝑆𝑆𝑁𝑁 𝑖𝑖𝑖𝑖

�𝑆𝑆𝑁𝑁 𝑜𝑜𝑜𝑜𝑜𝑜

Excess noise factor


Slide # 42

Sources of noise: Dark current shot noise

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PD

Gain 𝜇𝜇

𝐼𝐼𝐷𝐷

𝑡𝑡

𝑖𝑖2 = 2𝑒𝑒𝑒𝑒𝑒𝑒𝜇𝜇𝐼𝐼𝐷𝐷Dark current shot noise variance

𝐼𝐼𝐷𝐷


Slide # 43

Sources of noise: Photon shot noise

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PD

Gain 𝜇𝜇

𝐼𝐼 = 𝜇𝜇𝑃𝑃𝑆𝑆𝜆𝜆

𝑡𝑡

𝑖𝑖2 = 2𝑒𝑒𝑒𝑒𝑒𝑒𝜇𝜇𝐼𝐼 = 2𝑒𝑒𝑒𝑒𝑒𝑒𝜇𝜇2𝑃𝑃𝑆𝑆𝜆𝜆

Photon shot noise variance

𝐼𝐼


Slide # 44

Sources of noise: Johnson thermal noise

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𝑖𝑖

𝐼𝐼

𝑖𝑖2 =4𝑘𝑘𝑘𝑘𝑒𝑒𝑖𝑖

Johnson noise variance


Slide # 45

Detection signal-to-noise ratio (resistive termination)

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Sλ – Detector’s sensitivity

𝜇𝜇 – Detector’s intrinsic gain

ID – Detector’s dark current

F – Detector’s excess noise factor

B – Detection bandwidth

PB – Background light optical power

e – elementary charge; k – Boltzmann constant; T – temperature

𝑆𝑆𝑁𝑁

=𝑃𝑃 � 𝑆𝑆𝜆𝜆 � 𝜇𝜇

2𝑒𝑒𝑒𝑒 𝑃𝑃 + 𝑃𝑃𝐵𝐵 𝑆𝑆𝜆𝜆 + 𝐼𝐼𝐷𝐷 𝑒𝑒𝜇𝜇2 + 4𝑘𝑘𝑘𝑘𝑒𝑒𝑖𝑖

P – Instantaneous optical power


Slide # 46

Detection signal-to-noise ratio

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𝑆𝑆𝑁𝑁



𝑆𝑆𝑁𝑁

=𝑃𝑃 � 𝑆𝑆𝜆𝜆

2𝑒𝑒𝑒𝑒 𝑃𝑃 + 𝑃𝑃𝐵𝐵 𝑆𝑆𝜆𝜆 + 𝐼𝐼𝐷𝐷 𝑒𝑒

If the photodetector has a large intrinsic gain 𝜇𝜇, then the above equation for SN

reduces to:


(“large” intrinsic gain)

The effect of the intrinsic gain is to eliminate noise contribution from the front-end electronics.

Slide # 47

Closer look at the impact of photodetector gain

9/24/2019

𝑆𝑆𝑁𝑁


2𝑒𝑒𝑒𝑒 𝑃𝑃 + 𝑃𝑃𝐵𝐵 𝑆𝑆𝜆𝜆 + 𝐼𝐼𝐷𝐷 𝑒𝑒 + 4𝑘𝑘𝑘𝑘𝑒𝑒𝑖𝑖𝜇𝜇2

1. The purpose of the photodetector’s gain is to make the term 4𝑘𝑘𝑘𝑘𝐵𝐵𝑅𝑅𝜇𝜇2

negligible compared to the other noise terms.

2. For a given gain, the term 4𝑘𝑘𝑘𝑘𝐵𝐵𝑅𝑅𝜇𝜇2

can also be made smaller by increasing 𝑖𝑖.

3. (!!!) However, increasing 𝑖𝑖 may reduce detection bandwidth, reduce photodetector’s linearity, and cause electronics ringing (due to impedance mismatch).


Slide # 48

Closer look at the impact of photodetector gain

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The gain comes with excess noise factor, 𝑒𝑒.

PMT

APD

SiPM

105 − 107

105 − 106

1−100

𝑒𝑒𝜇𝜇

~1.2

~3 − 4

~1.1

𝑒𝑒 ≈𝛿𝛿

𝛿𝛿 − 1

𝑒𝑒 ≈ 𝜇𝜇0.3

𝑒𝑒 ≈ 1 + 𝑃𝑃𝑐𝑐𝑜𝑜


𝑆𝑆𝑁𝑁


2𝑒𝑒𝑒𝑒 𝑃𝑃 + 𝑃𝑃𝐵𝐵 𝑆𝑆𝜆𝜆 + 𝐼𝐼𝐷𝐷 𝑒𝑒 + 4𝑘𝑘𝑘𝑘𝑒𝑒𝑖𝑖𝜇𝜇2

Slide # 49

S/N comparison between photodetectors


1. In what follows, we compare the performance of four photodetectors given the same light input and front-end electronics.

2. Although not revealed, the photodetectors are those used in flow cytometry.

Slide # 50

Signal-to-Noise ratio: H10770A-40 PMT

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PMT (H10770A-40)

R = 10 kΩ

λ = 520 nm

Specifications

Photocathode spectral sensitivity SK at 520 nm = 175 mA/W

Gain μ = 5×105

Anode dark current ID = 3.3×10-9 A = 3.3 nA

Excess noise figure F ≈ 1.2

Maximum average anode current = 2 𝜇𝜇A

Temperature T = 20 ℃ = 293 K


Slide # 51

Signal-to-Noise ratio: S8664-30K APD

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APD (S8664-30K)

R = 10 kΩ

λ = 520 nm

Specifications

Spectral sensitivity σ at 520 nm = 0.34 A/W

Gain μ = 50

Dark current ID = 400 pA

Excess noise figure F ≈ 500.2 = 2.2



Slide # 52

Signal-to-Noise ratio: S3072 PIN PD

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PD (S3072)

R = 10 kΩ

λ = 520 nm

Specifications

Spectral sensitivity σ at 4520 nm = 0.35 A/W

Dark current ID = 0.3 nA (VR = 10 V)



Slide # 53

Signal-to-Noise ratio: S13360-3025CS SiPM

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SiPM (S13360-3025CS)

R = 10 kΩ

λ = 520 nm

Specifications

Photodetection efficiency at 520 nm η = 24%

Dark current ID = 44.8 nA


Gain μ = 7×105

Excess noise figure F ≈ 1.01

Number of microcells = 14,400


Slide # 54

Signal-to-noise ratio comparison


𝑖𝑖 = 10 𝑘𝑘Ω

PMT

SiPM

APD

PD

𝜏𝜏 = 520 𝑛𝑛𝑛𝑛

log10 𝑃𝑃 (Incident Power) [W]

log 1

0𝑆𝑆 𝑁𝑁

𝑒𝑒

Slide # 55



𝑖𝑖 = 10 𝑘𝑘Ω𝑃𝑃 = 1 𝑝𝑝𝑝𝑝

PMT

SiPM

APD

PD

This PMT has almost no sensitivity above 750 nm. However, there are other PMTs that have IR sensitivity.

Wavelength [nm]

log 1

0𝑆𝑆 𝑁𝑁

𝑒𝑒

Slide # 56

Importance of picking the right photocathode (PMT)


For a family of PMT photocathodes, the spectral response ranges from UV to IR.

Slide # 57



• As radiant incident power increases, 𝐵𝐵𝑁𝑁

for each photodetector increases and the intrinsic gain plays a less significant role.

𝑖𝑖 = 10 𝑘𝑘Ω

𝑃𝑃 = 1 𝑛𝑛𝑝𝑝

PMT

SiPM

APD

PD

Wavelength [nm]

log 1

0𝑆𝑆 𝑁𝑁

𝑒𝑒

Slide # 58

Signal shot noise limited case


𝑆𝑆𝑁𝑁



If 𝑃𝑃 is large so that the photon shot noise is dominant, the equation for 𝐵𝐵𝑁𝑁

becomes:

𝑆𝑆𝑁𝑁

=𝑃𝑃𝑆𝑆𝜆𝜆2𝑒𝑒𝑒𝑒𝑒𝑒 (signal shot-noise limited case)

Slide # 59

Comments on the S/N comparison


1. The above side-by-side comparison is not optimal. The performance of the detection system is not only a function of the photodetector but also of the front-end electronics: the two interact in a unique way. An optimal comparison would use font-end electronics for each photodetector that maximizes 𝐵𝐵

𝑁𝑁.

2. At a low incident power level, the PMT yields a higher 𝐵𝐵𝑁𝑁

than does the APD because of the PMT’s higher gain and lower dark current.

Slide # 60

Comments on the S/N comparison


3. At a higher incident power level, the performance of the APD, as measured by 𝐵𝐵𝑁𝑁

approaches that of the PMT.

4. The performance of the APD exceeds that of the PMT for wavelengths greater than about 750 nm. The PMT used in the above example has practically no sensitivity for wavelengths greater than about 750 nm.

Slide # 61

Desired characteristics of photodetectors: linearity and dynamic range

9/24/2019

Is the output proportional to the input?

PD E

• Linearity and dynamic range depend on the properties of the photodetector and detection electronics.

saturation


Slide # 62

Linearity and dynamic range


Input [Arb.]

Out

put [

Arb

.]

Range of measurable light levels (with dark

correction)

Range of outputs

Saturation

Ideal response

Range of measured outputs with S/N > 1

up to saturation

Slide # 63

Closer look at dynamic range for a PMT


Output current [mA]

Dev

iatio

n [%

]

H10720 10% nonlinearity: 75 mA, TP = 0.5 𝜇𝜇s

Gain = 2×106, QE = 28%

No. of incident photons at 450 nm per pulse:

4.2×105

• Dynamic range and linearity of a PMT can be controlled by the voltage divider.

Slide # 64

Closer look at dynamic range for a SiPM


𝑁𝑁𝛾𝛾 � 𝑃𝑃𝑃𝑃𝑃𝑃 = 1.1 × 105 (ideal response for 4.2 × 105 photons )

�𝑁𝑁𝑓𝑓𝑖𝑖𝑓𝑓𝑓𝑓𝑓𝑓 = 0.75 × 105 or 32% below an ideal response

𝑘𝑘𝑃𝑃 − Pulse duration

𝑡𝑡𝑓𝑓 − SiPM recovery time

�𝑁𝑁𝑓𝑓𝑖𝑖𝑓𝑓𝑓𝑓𝑓𝑓 −Average number of activated microcells

𝑁𝑁𝑜𝑜𝑜𝑜𝑜𝑜 − Total number of microcells

𝑁𝑁𝛾𝛾 − Number of photons in a pulse PDE − Photon detection efficiency

• Dynamic range and linearity of an SiPM is limited by the number of microcells.

Slide # 65

Dynamic range and linearity of a PD and APD


R

light

Photodiode or APD

𝑆𝑆𝑁𝑁

1. The lower bound of dynamic range is limited by the photodetector’s dark current shot noise and noise from the front-end electronics (resistor or TIA).

2. The upper bound of the dynamic range depends on the voltage bias (especially for photodiode), value of the load resistor, or dynamic range of the TIA.

3. The upper bound of the dynamic range of a photodiode and APD is generally larger than that for a PMT and SiPM.

Slide # 669/24/2019 Photodetection in Flow Cytometry


Forward-scatter signal Forward-scatter signal




Side

-sca

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Ideal Sample & Optics Variation Photon shot noise

QE conversion noise Gain variation noise Random electronic noise

Slide # 67

4. Summary and conclusions


1. Flow cytometry is a versatile technique to study cells and microparticles.

2. Photodetector is an indispensable component of every flow cytometer.

3. The choice of the photodetector should be based on the best 𝐵𝐵𝑁𝑁

performance of the detection system.

Slide # 68

4. Summary and conclusions


4. Limitations of the detection system will affect scatter plots and histograms masking or distorting science.

5. Idiosyncrasies of photodetectors prevent a simple swap of one detector for the other without altering the rest of the detection system.

Slide # 69Slide # 69

Thank You Fluorescence Microscopy Images

9/24/2019

Contact InformationSlawomir [email protected]


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Photodetection in Flow Cytometry - Hamamatsu Photonicshub.hamamatsu.com/sp/hc/resources/FC_Webinar.pdfSlide # 2 Outline 9/24/2019 Photodetection in Flow Cytometry 1. Introduction to