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 Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 2 Application Examples Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 3 Spectroscopy Techniques ■ 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. Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 4 Absorption Spectroscopy ■ 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 Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 5 Emission Spectroscopy ■ 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 Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 6 Spectrometer Selection 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) Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 7 Spectrometer Fundamentals Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 8 Spectroscopy -Creating Optical Spectrum ■ 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. Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 9 Spectrometer Operating Principles ■ 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. Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 10 Spectrometer Optical Resolution ■ 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) Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 11 Spectrometer Signal Considerations ■ 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. Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 12 Spectrometer Resolution & Slit Width Tradeoffs ■ 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 Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 13 Gaussian Fitting 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) Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 14 Optical Resolution, Distinguishing Spectral Features ■ 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). Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 15 Introduction of Opto-Electronic Terminology 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. Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 16 Explanation of Image Sensors Offset ■ 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 Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 17 Spectrometer Electronics Block Diagram (CCD) ■ 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) Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 18 Analog to Digital Converter Considerations ■ 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. Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 19 Analog to Digital Converter Considerations ■ 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 Hamamatsu Photonics K.K. and its affiliates All Rights Reserved. 20 Selecting Appropriate Bit-Depth ADC 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