Understanding Spectrometer Signal to Noise

John Gilmore, MSEE Hamamatsu Corporation

June 2020

 Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 1 ■ Application Examples ■ Spectrometer Fundamentals ■ Spectrometer Signal generation ■ Digital Data Considerations ■ Practical examples

■ Divided into two broad classes: absorption spectroscopy and

emission spectroscopy. Basic Idea of Absorption ■ In absorption spectroscopy, “known” Spectroscopy light illuminates the sample. The light may pass through (transmit) the “known” light illuminates the sample Sample “altered” light leaves the sample sample or reflect from it. The transmitted or reflected light differs from the “known” light. The change, among other factors, is a function of the sample’s chemical composition.

■ Each substance has a unique spectral signature. The output spectrum will show the absorption features only if the incoming illumination contains the wavelengths at for which absorption occurs.

퐼푙푙푢푚푖푛푎푡푖표푛 푆푝푒푐푡푟푢푚 AU= log( ) 푂푢푡푝푢푡 푆푝푒푐푡푟푢푚

■ The sample either produces its own luminescence or the external illumination (e.g., laser light) induces luminescence in the sample. The emitted light contains information a the sample’s chemical composition.

Basic Idea of Emission Spectroscopy

The sample produces its own light due to Emitted light contains information on high temperature, chemical reactions, Self-luminous chemical composition sample nuclear reactions, or some other luminescence process.

Emitted light contains information on External illumination induces chemical composition luminescence in the sample. Sample

Key Spectrometer Absorption Emission Spectroscopy Parameter Spectroscopy Wavelength & Optical Spectrometer meeting the application wavelength Resolution range and optical resolution Timing Lower scan rates, mSec Timing considerations, order and above excitation event (LIBS) SNR and Dynamic Range Detecting small changes Often times associated on a large signal. with low light conditions. Light Intensity Spectrometer with large Select spectrometer with signal to noise ratio low noise (readout noise)

■ In a dispersive spectroscopy, a dispersive element (e.g. prism or grating) takes in a beam of light from Basic Setup of Dispersive Spectroscopy the sample and separates the Dispersive element, e.g., Light from grating constituent wavelengths in angle. In the sample other words, it produces a spectrum. ■ Convolution of optical efficiency, Spectrum Recording device, photodetector quantum efficiency and e.g., CCD, CMOS, InGaAs Linear amplifier gain determine the signal.

■ Perform spectral separation. ─ Gratings ─ Fabry-Pérot Interferometer (FPI) ─ Michelson interferometer (FTIR) Spectrometer (Black Box) ■ Vast majority of grating based Input Light Output spectrometers use charge storage. (Photons) (Digital Data) ─ Q=CV=I*DT ■ FPI and FTIR generally use some Optics Electronics form of averaging ■ Ultimately supply digital data to micro-control or computer.

■ Ability to determine the natural widths of Often definite as Full Width Half Maximum (FWHM) individual emission lines and to distinguish neighboring peaks. f(l) ■ Spectral features smaller than the resolution cannot be directly distinguished. ■ Result of the spectrometers optical design and image sensor pixel size. ■ Resolution factors; ─ Slit Width

─ Grove density l1 l2 l ─ Focusing optics ─ Quality of components (aberrations)

■ Tradeoffs between light throughput, Wider slit often perceived as “sensitivity” and optical resolution. W ■ Larger slit wide, with sufficient fiber core, increase light collection. L ■ Optical power density, at spectrometer entrance slit, W/cm2 ■ Simple approximation as area of rectangle, L x W.

■ Higher resolution, meaning lower Spectrometer Resolution Changes 8 FWHM, enables the instrument to 7 better resolve narrow spectral lines 6 5 (peaks). 4 ■ The non-linear slit width, FWHM is 3 FWHM FWHM (nm) 2 caused by optical aberrations. 1 NA0.11, 250nm NA0.22, 250nm 0 0 50 100 150 200 Slit Width (um) Perfect lens without aberrations Lens with aberrations

NA0.11 NA0.22

Xe Lines ly 60000 NIR Spectrometer Xe Spectrum 50000 60000 40000 30000 50000 20000 10000

40000 Intensity(FS=65000) 0 970 975 980 985 990 995 1000 l 30000 x Wavelength (nm)

20000 Intensity (A/D Counts) (A/D Intensity 10000 Xe Line 8000 0 900 1000 1100 1200 1300 1400 1500 1600 1700 6000 4000 Wavelength (nm) 2000 lz

Intensity(FS=65000) 0 1075 1077 1079 1081 1083 1085 1087 1089 Wavelength (nm)

■ Mercury emission lines, known

doublet 576.9nm and 579.0nm Mercury Emission Spectrum ■ Intensity scale is normalized. 1 0.9 ■ Red is a spectrometer with 1nm 0.8 0.7 resolution. 0.6 0.5

0.4

■ Gray is a spectrometer with 5nm Intensity(Dark subtracted) 0.3 resolution. 0.2

0.1 Normalized 0 ■ Necessary to apply spectral fitting 572 574 576 578 580 582 584 techniques. Wavelength (nm) 1nm FWHM, slit width 10um 5nm FWHM, slit width 70um ■ Calculate Signal to Noise at each pixel (wavelength).

Parameter Brief Definition Readout Noise In image sensors, the readout noise is introduced when the charge packet is converted to a voltage by means of electronic amplifier. Unlike dark shot noise, readout noise is the fundamental noise source that cannot be eliminated. Full Well Capacity (FW) Also commonly referred to as saturation, full well capacity is the amount of charge (electrons) the image sensor (CCD) can handle. Dark Current Finite thermal carrier generated, by an image sensor, in the absence of light (photons). Dynamic Range (DR) Figure of merit as it is essentially an unachievable value. Calculated by dividing the Full Well Capacity by the Readout noise. Signal to Noise Ratio Differs from DR in that one determines the total noise at a given signal level. The (SNR) SNR is the signal divided by the noise at the signal level. Conversion Gain An image sensors ability to convert stored electrons to a voltage, by infernal (monolithic) or external amplification. Expressed in micro-volts per electron. Numerical Aperture (NA) In an optical system (lens), NA refers to the light acceptance cone.

■ Image sensor –Internal and external electronics create an offset. ■ Assure incoming analog signal is greater than zero.

Block diagram of a CMOS- Active Pixel image sensor

■ Analog Signal Processing Chain ■ Need to know; ─ Input voltage range of A/D ─ Resolution of A/D (12 bit, 16 bit) ─ Amplifier gain ─ Image sensor conversion factor Computer ─ Convert A/D Counts into Reflect the A/D counts ■ Reflect the A/D counts back to image sensor output ■ Determine system gain (e-/DN)

■ Sampling frequency – how often do we read the analog signal. ■ Quantization noise is the difference between the converted value and the actual. ■ ADC sampling rate must be at least twice the signal frequency. (Nyquist Criteria) ■ Image sensors and spectrometers- synchronize the ADC reading with the pixel ready timing.

■ ADC resolution, the number of steps used to digitally represent the analog signal. ■ Calculated as (2N – 1), where N is the bit depth.

Bit Depth Digital ADC Conversion Signal (FS=3.3V) 8 255 12,941uV/DN

12 4095 805.9uV/DN

16 65,535 50.3uV/DN

24 16,777,215 19.7uV/DN

Part Full Well Readout Noise Dynamic Maximum Sufficient Comment Number Range Signal to ADC Noise S10121 165pC ~ 10,000e- RMS 103K 32,000 2 18 = An 18 bit converter is twice (CMOS-PDA) ~1030Me- (depends on 262,144 the sensors dynamic range. circuit designer) (18 bit ADC) S10420 Horizontal 6e- rms 50K 550 2 16 = 65536 16 bit ADC is greater than (BT-CCD) 300Ke- sensor dynamic range. S11639-01 2V/(25uV/e-) 0.4mV/(25uV/e-) 5K 280 2 12 = 4096 A 12-bit converter almost (CMOS-APS) ~80Ke- ~16e-rms coverts the sensors dynamic range, but for marketing reasons, almost no one uses a 12-bit ADC.

■ Charge is stored in the feedback capacitance of charge amplifier. ■ Charge is integrated over a period of time, InGaAs this is known as the integration time or exposure time. ■ Readout noise represents the noise floor. ■ Within any given spectrometer there is an 푡1 offset. 푄 = 퐶푉 = න 퐼 푡 푑푡 푡0 ■ I(t) = IL + ID ■ Increase input slit width to allow more light to enter. Q = CV = I * Dt

푆푖푔푛푎푙 = 푃푖 ∗ 푆푠 ∗ ∆푇 Integration time Spectrometer Sensitivity Optical power

퐶표푢푛푡푠 푆푖푔푛푎푙 = { } ∗ 푊푎푡푡푠 ∗ 푆푒푐 Watts and Sec cancel, left with Counts 푊푎푡푡푠 ∗ 푆푒푐

■ Spectrometer sensitivity (Ss ) expressed in units of; {Counts/(Watt*Sec)}

푆푖푔푛푎푙 = 푃푖 ∗ 푆푠 ∗ ∆푇 푆푖푔푛푎푙 = 4푥1017(퐶표푢푛푡푠Τ푊푎푡푡푠 ∗ 푆푒푐) ∗ 1푝푊 ∗ 100푚푆푒푐 푆푖푔푛푎푙 = 40,000 AD Counts

■ Offset is a fixed value to assure spectrometer output is always greater than zero. ■ Because it’s a constant, offset does not contribute to shot noise. ■ Dark signal (dark current) is above the offset. ─ Practical tip- use minimum integration setting to approximate the offset.

■ Image sensor output and A/D considerations CCD Full Well Or

■ Understand does the image Image Sensor Output Range InGaAs Saturation Charge sensor reach saturation before the A/D? ■ Reverse scenario, A/D saturates before the image sensor?

CCD Full Well Or InGaAs Saturation Charge

CCD Full Well Image Sensor Output Range Or Image Sensor Output Range InGaAs Saturation Charge

Left – Image sensor dynamic range Right – Image sensor dynamic range matched within the limits of A/D full scale. exceeds the limits of A/D full scale.

 Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 30 Total Noise 0 0 ■ Shot noise follows Poisson 2 2 2 2 푁푡 = 푁푟 + 푁푑 + 푁푝 + 푁푠푦푠 distribution. Nr – Readout Noise ■ Discrete nature of electrons and Nd – Dark shot noise photons. Np – photon shot noise Nsys – System noise ■ Noise analysis based on ideal 2 2 optics as first order. 푁푡푑 = 푁푟 + 푁푑 ─ Stray Light can also introduce noise. Ntd – Total Dark Noise ■ ADC quantization noise. ─ Not an issue with proper electrical design. Shot noise can be calculated by taking the square root of the number of electronics, following Poisson distribution. Only when converted to electronics. One cannot take the square root of AD counts correctly compute noise.

C13555MA ■ UV-Visible spectrometer using Average Dark Output 9500 CMOS-APS technology. 8500 7500

■ Black box – 16 bit ADC with 6500 USB interface. 5500

Output A/D OutputA/D Counts 4500

3500 ■ Acquire 100 readings at each 0.00001 0.0001 0.001 0.01 0.1 1 Exposure Time (Sec) exposure time, calculate the C13555MA average value and the standard Total Dark Noise 120 deviation (noise). 100 80

■ Benefit of performing dark noise 60 analysis as a bench mark. 40 20

Output A/D OutputA/D Counts (RMS) 0 0.00001 0.0001 0.001 0.01 0.1 1 Exposure Time (Sec)

C10082CAH ■ UV-Visible spectrometer using Average Dark Output 1600 1400 BT-CCD technology. 1200

Counts 1000 ■ Black box – 16 bit ADC with 800 600 400 USB interface. Output A/D 200 0 ■ Acquire 100 readings at each 0.01 0.1 1 Exposure Time (Sec) exposure time, calculate the C10082CAH average value and the standard Total Dark Noise 25

deviation (noise). 20 ■ Dark output non-linear due to 15 10

spectrometer offset. 5 Output A/D Counts(RMS) 0 0.01 0.1 1 Exposure Time (Sec)

■ Represents the instrument or systems accuracy. ■ Signal to Noise must be greater than unity. ■ No dimensions –Ratio ■ The larger the SNR, the more precisely measurements. ■ Provides a uniform comparison amongst spectrometers / manufacturers.

Sm = 푃푖 ∗ 푆푠 ∗ ∆푇

Sm - Measured Signal = 푆푠 − 퐷푎푟푘 + 푂푓푓푠푒푡 푁푡 = 2푁푟2 + 푁푑2 + 푁푝2 + 푁푠푦푠2

Nr – Each readout sequence contains readout noise. To calculate the absolute signal measured value, the different between two readings are taken (Signal+Dark+offset) and (Dark+Offset). This introduces a factor of 2 read noise. Nd – Dark shot noise Np – (Photo-electrons + Dark electrons + Offset) ; Shot noise is included in the dark electronics and must be included to accurately calculate the total noise. Nsys – System noise, light source drift, temperature changes, etc.

5V/ 216 = 76uV/DN S10420-xxxx (BT-CCD) Conversion Gain = Amplifier ADC

6.5uV/e- Image Sensor Image A/D Converter; Amplifier Gain = 3.5 16 bits  216 = 65636 Input range 0  5V

푢푉 퐴퐷퐶 퐶표푛푣푒푟푠푖표푛 ൗ퐴푚푝 퐺푎푖푛 퐷푁 푆푦푠푡푒푚 퐺푎푖푛 = 퐶표푛푣푒푟푠푖표푛 퐺푎푖푛 (푢푉Τ푒− )

푢푉 76 퐷푁 ൗ3.5) −Τ = 6.5 (푢푉Τ푒−) = 3.35 (푒 퐷푁)

Optical Fiber Shutter Iris ■ Procedure Halogen Spectrometer ─ Verify lamp stability Lamp ─ Set exposure time to minimum value. ■ Equipment ─ Adjust light intensity, vary iris ─ Halogen lamp (maintain color temperature). ─ Optical fiber ─ Semi-automated data collection ─ Optical attenuator (iris) routine, minimum 100 spectra. ─ Spectrometer ─ Calculate average signal at each pixel (wavelength). ─ Computer ─ Compute the standard deviation (noise) at each pixel.

Spectral Data ■ Average signal over spectrometers Ti=1mSec, 50 spectrum 400 70000 wavelength range (all pixels) 350 60000 300 50000 250 40000 ■ Each wavelength (pixel) corresponds to 200 30000

150 Dark (A/D Counts) 100 20000 -

varying signal levels. 50 10000 Signal

Noise Noise SNR & Counts) (A/D 0 0

566 358 385 410 434 457 480 502 524 545 587 608 628 648 668 687 706 724 743 760 778 795 813 830 ■ Maximum SNR occurs in the region of 330 Wavelength (nm)

highest signal level, ~700nm. SNR Noise Avg Signal

■ Low signal levels, as signal increases, the Signal to Noise Plot (Photon Transfer) 1000 total noise remains fairly constant. An indication total noise dominated by readout 100 noise. Noise Floor ■ As signal increases, we see the total noise Noise Counts) (A/D 10 becomes dominated by photon shot noise. 100 1000 10000 100000 Signal (A/D Counts)  Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 39 Measured Examples of Signal vs Noise (Photon Transfer)

■ The plateau (flat) region, dominate noise is circuit noise, readout noise. ■ As the signal increase we see the impact of photon shot noise, giving rise to total noise. ■ Blue – BT-CCD, noise floor on the order of 20-30e-

Signal to Noise, Digital Summing 50 Spectrum ■ Summing multiple spectrum. 10000 ■ Signal is additive.

■ Readout noise will also increase. 1000 Noise (electrons RMS) Noise (electrons Signal to Noise Comparison 100 1800 10000 100000 1000000 10000000 1600 Signal (electrons RMS)

1400

1200 Signal to Noise Plot 1000 1000 SNR 800

600

400

200 100 0 300 400 500 600 700 800

Wavelength (nm) Noise (electrons RMS)

Total Noise ■ 3D surface plot showing peak intensity contained in the peak signal fluctuations (noise) over time. ■ Peak signal, an average of 100 scans. ■ Calculate the total noise contained in each pixel (wavelength), this includes dark current.

C11697MA Hg-Ar Spectrum C11697MA Hg-Ar Spectrum Ti=5.5mSec Ti=5.5mSec 40 350

38 300 36 250 34

32 200

150 SNR

TotalNoise 28 100 26

24 50

22 0 20 355 360 365 370 375 355 360 365 370 375 -50 Wavelength (nm) Wavelength (nm)

Total measured noise Signal to Noise Ratio `~ 300

■ Constant illumination source, NIR Spectral Analysis, C9913GC, Ti=2150uSec acquire consecutive 100 spectrum. 1.0007 60000

■ Maximum signal to noise occurs at 1.0005 50000

highest signal level. 1.0003 40000

■ Ideally we are operating within a 1.0001 30000 Ratio (I/Io)

0.9999 20000

Photon Shot noise limit. Intensity (A/D Counts)

■ Highlighted region of interest 0.9997 10000

represents the expected highest 0.9995 0

65 17 33 49 81 97

273 481 113 129 145 161 177 193 209 225 241 257 289 305 321 337 353 369 385 401 417 433 449 465 497 SNR Pixel Number (900nm-1700nm) ■ Where is the noise the largest? ■ What is the noise on the edges?

Example of Stray Light ■ Narrow down noise source. Dark Subtration, Monochrometer 100um slit width (0.23nm) 1 ─ Check dark noise performance? ─ Plot temporal distribution (signal vs time). 0.1 ■ Assess spectrometer stray light

contributions. 0.01 400nm 500nm ─ Light wonders to unexpected region. 600nm 700nm ■ What impact does temperature 0.001

800nm NormalizedAbsolute Value have on your measurements? 900nm ─ Keep measurement interval as short 0.0001 as possible to minimize the impact of temperature drift. 0.00001 300 400 500 600 700 800 Wavelength (nm)

■ What impact does temperature Temporal Stability (Drift) have on your measurements? 49300

─ Keep measurement interval as short 49200 as possible to minimize the impact of temperature drift. 49100

49000

1280.17

48900 Intensity (A/D Counts) 48800

48700

48600 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 Time

■ Signal to Noise is one of the most important parameters to consider when performing spectroscopic analysis. ■ Many factors involved with SNR analysis. ■ Measured data and analysis need to be carefully considered for accurate results. ■ For single scan applications, the maximum SNR is the square root of the number of electronics.

Week # Weekly Topics # of Talks Talk #1 Date Talk #2 Date 1 Introduction to Photodetectors 2 26-May-20 28-May-20 2 Emerging Applications - LiDAR & Flow Cytometry 2 2-Jun-20 4-Jun-20 3 Understanding Spectrometer 2 9-Jun-20 11-Jun-20 1 Weeks Break 4 Specialty Products – Introduction to Light Sources & X-Ray 2 23-Jun-20 25-Jun-20 5 Introduction to Image Sensors 2 30-Jun-20 02-Jul-20 1 Weeks Break 6 Specialty Products – Laser Driven Light Sources 2 14-Jul-20 16-Jul-20 7 Image Sensor Circuits and Scientific Camera 2 21-Jul-20 23-Jul-20 8 Mid-Infrared (MIR) Technologies & Applications 2 28-Jul-20 30-Jul-20 1 Weeks Break 9 Photon Counting Detectors – SiPM and SPAD 1 11-Aug-20 10 Using SNR Simulation to Select a Photodetector 1 18-Aug-20 To register and attend other webinar series, please visit link below: https://www.hamamatsu.com/us/en/news/event/2020/20200526220000.html  Hamamatsu Photonics K.K. and its affiliates. All Rights Reserved. 48  Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 49