ABSTRACT. We further show that using pixel variance for flat field correction leads to errors in cameras with good factory calibration.

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1 Quntittive evlution of the ccurcy nd vrince of individul pixels in scientific CMOS (scmos) cmer for computtionl imging Shigeo Wtne*, Teruo Tkhshi, Keith Bennett Systems Division, Hmmtsu Photonics K.K. 812, Joko-cho, Hmmtsu City, JAPAN ABSTRACT The scientific CMOS (scmos) cmer rchitecture fundmentlly differs from CCD nd EMCCD cmers. In digitl CCD nd EMCCD cmers, conversion from chrge to the digitl output is generlly through single electronic chin, nd the red noise nd the conversion fctor from photoelectrons to digitl outputs re highly uniform for ll pixels, lthough quntum efficiency my sptilly vry. In CMOS cmers, the chrge to voltge conversion is seprte for ech pixel nd ech column hs independent mplifiers nd nlog-to-digitl converters, in ddition to possile pixel-to-pixel vrition in quntum efficiency. The rw output from the CMOS imge sensor includes pixel-to-pixel vriility in the red noise, electronic gin, offset nd drk current. Scientific cmer mnufcturers digitlly compenste the rw signl from the CMOS imge sensors to provide usle imges. Sttisticl noise in imges, unless properly modeled, cn introduce errors in methods such s fluctution correltion spectroscopy or computtionl imging, for exmple, locliztion microscopy using mximum likelihood estimtion. We mesured the distriutions nd sptil mps of individul pixel offset, drk current, red noise, linerity, photoresponse non-uniformity nd vrince distriutions of individul pixels for stndrd, off-the-shelf Hmmtsu ORCA-Flsh4.0 V3 scmos cmers using highly uniform nd controlled illumintion conditions, from drk conditions to multiple low light levels etween ~20 to ~1,000 photons / pixel per frme to higher light conditions. We further show tht using pixel vrince for flt field correction leds to errors in cmers with good fctory clirtion. Keywords: scmos cmer, photoresponse uniformity, vrince mp, photoresponse linerity, drk offset 1. INTRODUCTION A scientific cmer should ccurtely detect the numer of input photons nd the digitl output signl should fithfully represent the numer of input photons, nd provide not only pretty picture, ut lso predictle noise sttistics. Scientific CMOS (scmos) cmers re incresingly used for iologicl reserch. In terms of the quntittive properties of signl detection, the scmos cmer rchitecture fundmentlly differs from CCD nd EMCCD cmers. In scientific digitl CCD nd EMCCD cmers, conversion from chrge to the digitl output is generlly through single electronic chin, nd the red noise nd the conversion fctor from photoelectrons to digitl outputs is highly uniform for ll pixels, lthough quntum efficiency my sptilly vry. By contrst, in CMOS cmers, the chrge to voltge conversion is seprte for ech pixel, ech column hs independent mplifiers nd nlog-to-digitl converters, nd microlenses introduce pixel-to-pixel vrition in quntum efficiency. The rw output from the CMOS imge sensor includes pixel-to-pixel vriility in the red noise, gin, offset nd drk current. Therefore, scientific cmer mnufcturers must digitlly compenste the rw signl from the CMOS imge sensors 1, 2. Unless corrected, inccurcies nd noise in imge cn introduce rtifcts in computtionl imging such s locliztion microscopy, especilly in the cse of mximum likelihood estimtion methods 3, 4. *shigeo-w@sys.hpk.co.jp Single Molecule Spectroscopy nd Superresolution Imging X, edited y Jörg Enderlein, Ingo Gregor, Zygmunt Krol Gryczynski, Riner Erdmnn, Felix Koerling, Proc. of SPIE Vol , Z 2017 SPIE CCC code: /17/$18 doi: / Proc. of SPIE Vol Z-1

2 The recently relesed Hmmtsu ORCA-Flsh4.0 V3 hs well-clirted pixel response nd predictle individul pixel sttistics. In this pper we show tht this cmer (pek QE, 82%) is ccurtely fctory-clirted t the individul pixel level for drk offset nd gin, is highly liner cross the entire signl rnge, nd tht individul pixel vrince cn e ccurtely modeled s sum of two pixel-specific terms: red noise nd vrince coefficient tht is multiplied y the signl in the pixel (primrily from shot noise). 2.1 DSNU (Drk signl non-uniformity) 2. DSNU AND DARK CURRENT MEASUREMENT We mesured the drk signl non-uniformity to estlish the stility nd uniformity of the cmer offset. To reduce the effects of sttisticl error, 20,000 frmes, cptured with the light-tight cp on, were collected with 10 msec exposure time t 100 Hz frme rte (stndrd scn mode of ORCA-Flsh4.0 V3). The verged DSNU mp (2,000 x 2,000 pixels region out of 2,048 x 2,048 full frme size) is shown in Figure 1. To emphsize the residul offset nonuniformity, dt for ech pixel ws verged for 20,000 frmes, nd nrrow look-up-tle used for visuliztion. Smll differences in the columns re visile in the imges. The histogrm of DSNU pixel distriution is shown in Figure 1. The men pixel response is 99.6 DN (digitl numer, 45.8 e - in electron units) nd the SD (stndrd devition) is 0.61 DN (0.28 e-). Furthermore, to show the uniformity of DSNU, 3-level threshold visuliztion ws used: lue represents pixels within ±2 DN (0.92 e - ) of the men, while green nd red pixels represent those less thn -2 DN or greter thn +2 DN from the men, respectively. 98.6% (3,942,153/4,000,000) of the pixels re within ±2 DN (0.92 e - ) of the men, showing the excellent uniformity of the ORCA-Flsh4.0 V3 s offset i o5 104 Log -liner histogrm of verged drk imge Men = 99.6 DN = 45.8e SD = 0.61 DN = 0.28e 50 x 50 pixels 100 i Averged drk imge horn 20,000 frmes pixels 10 msec exposure Stndrdscn me [DN] [el c x 50 pixels 100 ô z " SD within men # 0.92 ev DN) = 0.52 DN = 0.24 e Pixels within men # 0.92 eje DN) = / Frction within men ± 0.92 e-12 DN) = 98.6 % Figure 1. DSNU ) mp, ) offset histogrm nd c) threshold mp of pixels >2 DN (0.92 e - ) from the men. 2.2 Drk current Drk current influences imge qulity. A mp of the pixel-specific drk current, sed upon 999-second exposure is shown in Figure 2. Drk current is distriuted uniformly except ner the four corners, where the drk current is higher due to the circuit structure. The histogrm of drk current is shown in Figure 2. The men vlue of the Proc. of SPIE Vol Z-2

3 drk current in the centrl 1,500 x 1,500 pixels re is 0.07 e - /sec, excluding few outliers (-100<DN<5,000) with SD 0.18 e - /sec. 999 sec integrtion drk imge 999 sec integrtion drk imge histogrm tos Z 2048 x 2048 pixels DN, offset sutrcted DN Men: e- /sec (- 100 <DN <5000) = 0.18 e- /sec Sttics in 1500x1500 re DN, offset sutrcted Figure 2. ) Drk current sptil distriution nd ) histogrm. 3.1 PRNU (Photoresponse non-uniformity) 3. PRNU AND LINEARITY We mesured the photoresponse non-uniformity (PRNU) nd linerity of severl scmos cmers. PRNU t oth low light (693 e - ) nd t higher light (4,560 to 23,023 e-) levels were mesured. In the low light rnge, 20,000 frmes Low light rnge (High gin mplifier) 1508 DN = 694 e- men illumintion(1500x1500) 128x x2000 Normlized verged imge from frmes High light rnge (Low gin mplifier) DN = e' men illumintion(1500x1500) Irrrrrr 128x x x2000 Normlized verged imge from 1000 frmes Log -liner histogrm of pixel response under uniform illumintion 10 10'. io' 1500 x 1500 re used for sttics Log -liner histogrm of pixel response under uniform illumintion ms o' 'or 10' 1o, Reltive pixel response _ I Reltive pixel response DN in 1500x1500 ROI Photoelectron(e )= 694 e Men= 1.00 RMS= 1.00 SD = PRNU = 0.27% 9914 DN in 1500x1500 ROI Photoelectron(e) = 4561 e Men= 1.00 RMS= 1.00 SD = PRNU = 0.11% DN in 1500x1500 ROI Photoelectron(e )= e Men= 1.00 RMS= 1.00 SD = PRNU = 0.062% DN in 1500x1500 ROI Photoelectron(e) = e Men= 1.00 RMS= 1.00 SD = PRNU = 0.083% Figure 3. ) PRNU nd ) log-liner histogrms of pixel response uniformity in oth low nd high light rnges. Proc. of SPIE Vol Z-3

4 were cptured nd verged. At high light rnge, 1,000 frmes were cptured nd verged. Typicl PRNU mps of the low light rnge nd high light rnge re shown in Figure 3. A 1,500 x 1,500 re pixel dt from ech light level is used for sttisticl nlysis. Log-liner histogrms of pixel response under oth low light nd high light illumintion re shown in Figure 3. We define the PRNU vlue s the SD of pixel response under uniform illumintion. The PRNU t low light level (1,507 DN = 693 e-) is 0.27% while PRNU t high light levels (9,914 DN, 32,686 DN nd 50,050 DN) re 0.11%, 0.062% nd 0.083%, respectively, with pproximtely Gussin distriutions. 3.2 Linerity The ORCA-Flsh4.0 V3 scmos cmer uses two mplifiers: high gin mplifier for low input signls (elow out 2000 DN) nd low gin mplifier for higher input signls. For oth the high gin mplifier nd low gin mplifier, we mesured the photoresponse linerity y chnging the exposure time t fixed, highly uniform illumintion intensity. Figure 4 plots the DN ginst the light exposure nd plot of frctionl error, which is the difference etween the mesured signls normlized to the totl illumintion (the product of light intensity nd exposure time) t low light level from 100 DN to 1000 DN nd the est liner fit. We used modified EMVA 1288 stndrd to provide quntittive mesurement of the linerity of the high gin mplifier. The stndrd EMVA 1288 definition of linerity error fits stright line of the output to the input, mesures the error t lest 10 points from 5% to 95% of mximum specified full scle signl in 10% increments, nd then verges the mximum nd minimum errors nd divides y 90% Linerity, low light rnge, 3 different cmers o Exposure time (msec) Exposure time (msec) Frctionl error (%): sed on modified EMVA1288 stndrd. 100% is light rnge ( DN). Cmer_1 Cmer_2 Cmer_3 Linerity error = 0.14 Linerity error = 0.17 Linerity error = 0.16 Linerity = 99.86% Linerity = 99.83% Linerity = 99.84% Linerity, full light rnge, 3 different cmers o - O o 8o LL Exposure time (msec) m Exposure time (msec) Frctionl error (%) sed on EMVA1288 stndrd Cmer_2 Cmer_3 Cmer_4 Linerity error = 0.39% Linerity error = 0.38% Linerity error = 0.33% Linerity = 99.61% Linerity = 99.62% Linerity = 99.67% Figure 4. Linerity of 3 different cmers in oth ) low nd ) high light rnges. Proc. of SPIE Vol Z-4

5 of full scle. As the high gin mplifier output is entirely elow 5% of the full rnge of the cmer, we modified the definition for the high gin mplifier to use the mesured intensity rnge s the full scle for mesurements of linerity of this mplifier, nd retined the conventionl definition for the low gin mplifier. The linerity results of three cmers t low light rnge re shown in Figure 4, nd re 0.14%, 0.17% nd 0.16% linerity error using the modified EMVA definition. The photoresponse linerity over the full light rnge ws mesured following the EMVA 1288 stndrd. The linerity results of three cmers t full light rnge re shown in Figure 4 in the sme mnner s low light rnge dt. The linerity errors of three different cmers t full light rnge re 0.39%, 0.38% nd 0.33% 3.3 Asolute response error t vrious light levels Here we nlyzed the solute response error t vrious low light levels to illustrte the quntittive ccurcy of the scmos cmer, which is the rnge tht mny iologicl reserchers use. At ech intensity level we mesured the solute error of the output from ech pixel. The solute error is the difference etween the vlue recorded in ech pixel nd the men vlue of ll pixels in 2,048 x 2,048 re under highly uniform (+0.1%) illumintion. Histogrms of the solute error t ech intensity level re shown in Figure 5. Figure 5 shows the frction of pixels, within specific tolernce levels t vrious input intensities. More thn 85% of individul pixels show n solute error of less thn 1.0% of the signl + offset error of less thn 0.91 photons equivlent (1.4 DN x 0.52 [e - /DN]/ 0.8 [e - /photon], the offset error of 97% of pixels re within +1.4 DN) t ll light levels. In other words, for n input signl of 200 photons, 85% of the pixels hve solute error of less thn 3 photons. 2.5 x105 2 i 1.5 c m S m 1 IL 05 o -10 Histogrm of Error for ll pixels t ech light level Offset AI pixel verge oflsigl- 34Ú?4 o`fsetl [DN] w I:: - T, x 0.7 ±1.4DN (0.91 photon) ± 1.0% - ±1ADN (0.91 photon) ± 0.5% QE =Os ±1.4DN (0.91 photon) ± 0.2% LL s CF=0.52(é/ON)=1/gin Asolute error (Pixel signl - men signl) [Photons] All pixel verge of (signl - offset) [DN] Figure 5. ) Distriution of solute response error t vrious light levels nd ) frction of pixels within specified tolernce levels. 4. TEMPORAL READOUT NOISE AND VARIANCE MODEL 4.1 Temporl redout noise By mesuring the vrince of ech pixel from 1,000 frmes of dt, we estimted the temporl drk red noise of the ORCA-Flsh4.0 V3 scmos cmer. A red noise mp of stndrd scn mode is shown in Figure 6. The pixelspecific red noise is generlly uniformly distriuted over the entire imge re. Log-liner histogrms of the red noise (squre root of the drk vrince) for oth stndrd scn mode nd slow scn modes re shown in Figure 6. In stndrd scn mode (10 μs/row redout rte), the men, RMS nd medin vlues of the red noise re 1.31, 1.62 nd 0.99 e -, respectively. In slow scn mode (30 μs/row redout rte), the men, RMS nd medin vlues of the red noise re 1.13, 1.48 nd 0.82 e -, respectively, consistent with the cmer specifictions. Proc. of SPIE Vol Z-5

6 Red noise mp Stndrd scn mode Men = 1.31 RMS = 1.62 Medin= 0.99 Slow scn mode 2000 x 2000 pixels Stndrd scn mode Men = 1.13 RMS = 1.48 Medin= Figure 6. Pixel-specific temporl drk red noise of ORCA-Flsh4.0 V3 scmos cmer. 4.2 Vrince model The vrince of pixel response under stle illumintion is importnt for dt nlysis tht utilizes sttisticl methods, for exmple, mximum likelihood nlysis for super resolution single molecule locliztion microscopy 4. The vrince of specific pixel is pproximtely estimted y the sum of the drk vrince (red noise) nd constnt (K) times the output signl. To first order, good estimte of the vrince of pixel is the sum of the drk vrince (red noise squred) of ech pixel plus signl-dependent term (rising from photoelectron shot noise) given y the product of constnt times the output of the pixel, i.e. vrince = rednoise 2 xy + K * S, where rednoise 2 xy is the pixel vrince in the drk, K is constnt, which we term the vrince coefficient, nd S is the mesured signl 5. However, more ccurte estimte requires determintion of the constnt K xy for ech pixel. To find the est estimtion for pixel vrince, we exmined the reltionship etween the vrince nd the output signl of ech pixel y cpturing 20,000 imge frmes (10 msec intervl) in the drk nd t ech of eight (8) different low light levels using highly stle nd uniform illumintion system. The vrince of pixel is modeled using the photon trnsfer curve eqution 5 s (Vrince xy = K xy *(Signl xy - Offset xy ) + rednoise 2 xy). We estimted K xy using weighted lest squres fitting of the vrince for ech pixel t ech of the light levels. The slope of the est-fit line is good estimte of K xy. A mp of K xy (2,048 x 2,048 pixels re) nd ssocited histogrm re shown in Figure 7. In n idel photon trnsfer curve model, the K xy vlue is simply the pixel gin vlue. However, s this K xy mp clerly shows, slight vritions re pprent in the upper nd lower prts of the mp nd lso some verticl stripes ssocited with the column mplifiers. This mp is qulittively nd quntittively different from the PRNU mp of Figure 3. Therefore, the K xy vlue is not precisely equl to pixel response correction, nd therefore estimtion of pixel gin y mesuring the vrince results in inccurte flt field correction estimtions. In mny cses, pixel-specific red noise with uniform vrince coefficient K provides good enough estimte for sttisticl weighting. However, if more ccurte estimte of the pixel-specific vrince is needed, mesurement of the pixel-specific vrince coefficient (K xy ) is required. To determine the ccurcy with which the vrince of pixel t specific illumintion cn e estimted using pixel-specific vlues for the red noise nd vrince coefficient, the frctionl error in K xy for ech light intensity is clculted from the eqution of (mesured K xy t ech light level est fit vlue) / men K xy. The histogrms of K xy error t vrious verge mesured intensity levels re shown in Figure 7. The distriution of K xy is quite uniform for every light intensity except the lowest light intensity, nd the width of the histogrm (Figure 7) of the frctionl error etween the mesured vlue of K xy t ech light level nd the est fit vlue of K xy (over 9 light levels) is nrrower thn the histogrm (Figure 7) of K xy, normlized y its men vlue (~2). This dt suggests tht the vrince for ech pixel cn e estimted t ny light intensity with resonle ccurcy, enling the correct estimtion of vrince in ech pixel over rnge of signl intensities. Note tht these mesurements require n extremely stle light source, preferly with highly uniform intensity distriution cross the imge sensor. Proc. of SPIE Vol Z-6

7 Vrince coefficient (K2y) mp Histogrm of Vrince coefficient (K2y) D N /e Vrince = K *(Signl Offset y) + rednoise2 K fit using weighted lest squre t 9 light level frmes t ech light level 2048x2048 Histogrm of KxY Error for ll pixels t ech light level 10 X105 Sttisticl mesurement precision limit All pixel verge of (signl - offset) [DN] , KxY Error (mesured vrince- fitted vrince) [rte] Figure 7. ) Vrince coefficient mp, ) histogrm of vrince coefficient K xy nd residul K xy error s function of light level. The curve leled Sttisticl mesurement precision limit shows the sttisticl uncertinty in mesurement of the vrince of single pixel using 20,000 mesurements rising solely from sttisticl considertions. The center is offset to enhnce visiility. 5. CONCLUSIONS AND DISCUSSION We crefully chrcterized stndrd-production Hmmtsu ORCA-Flsh4.0 V3 scmos cmers for offset uniformity, photoresponse non-uniformity, linerity, drk current uniformity, red noise nd vrince coefficient, including histogrms nd ssocited sptil distriutions of ech prmeter. These cmers with on-ord correction hve excellent drk offset uniformity. Compenstion for oth QE nd electronic gin vrition through the flt field clirtion process results in photoresponse uniformity (0.06 % rms), etter thn front-illuminted CCDs (0.25%, typicl) nd much etter thn ck-illuminted imge sensors (e.g. EMCCD, or ck-illuminted CCDs) which hve spectrlly dependent PRNU (>1% rms typicl for nrrownd light) 6. We showed the cmer linerity over oth the low light nd full light rnges. In prticulr, the input intensity (photons) for ech pixel cn e estimted from the cmer output t low light level with high fidelity. The vrince coefficient mp, which indictes the signl-dependent contriution to the pixel vrince (from shot noise), is estimted y mesuring the vrince of ech pixel in the drk nd t severl light levels. This vrince coefficient mp is qulittively nd quntittively different from the photoresponse mp, indicting tht the vrince coefficient, which is often thought to e equl to gin, is in fct prtilly independent prmeter. Proc. of SPIE Vol Z-7

8 Only direct flt field mesurement using known (preferly uniform) light source cn e used to correct for pixel response inhomogeneity, which rises from the comintion of pixel (nd potentilly wvelength) dependent quntum efficiency nd electronic gin. In the cse of ck-illuminted imge sensors for which the quntum efficiency my e strongly wvelength dependent, the detected signl must e similr to the illumintion used for flt field correction. Using pixel vrince to estimte pixel-specific gin leds to incorrect cmer clirtions. Direct fctory clirtions re more ccurte. ORCA-Flsh4.0 V3 specifiction Drk Signl Non-Uniformity (DSNU) e - rms Photoresponse Non-Uniformity (PRNU) t hlf level of full 0.06 % rms light rnge (15,000 e - ) 1 Photoresponse Non-Uniformity (PRNU) t low light level 0.3 % rms (700 e - ) 1 Linerity error, full light rnge (EMVA 1288 stndrd) % Linerity error, low light rnge (<500 e - signl) % / Less thn pprox. 1 e- solute error Drk Current (electrons/pixel/s) Air Cooled to -10 C 0.06 Redout Noise (Nr) medin in electrons t slow scn Redout Noise (Nr) rms in electrons t slow scn Redout Noise (Nr) medin in electrons t stndrd scn Redout Noise (Nr) rms in electrons t stndrd scn Typicl vlue REFERENCES [1] Fullerton, S., Bennett, K., Tod, E., Tkhshi, T., Cmer simultion engine enles efficient system optimiztion for super-resolution imging, Proc. SPIE 8228, Single Molecule Spectroscopy nd Superresolution Imging V, (2012). [2] Fullerton, S., Bennett, K., Tod, E., Tkhshi, T., Optimiztion of Precision Locliztion Microscopy using CMOS Cmer Technology, Proc. SPIE 8228, Single Molecule Spectroscopy nd Superresolution Imging V, 82280T (2012). [3] Hung, Z. L., Zhu, H., Long, F., M, H., Qin, L., Liu, Y., Ding, J., Zhng, Z., Luo, Q., Zeng, S., Locliztion-sed super-resolution microscopy with n scmos cmer, Optics Express 19(20), (2011). [4] Hung, F., Hrtwich, T. M., River-Molin, F. E., Lin, Y., Duim, W. C., Long, J. J., Uchil, P. D., Myers, J. R., Bird, M. A., Mothes, W., Dvidson, M. W., Toomre, D., Bewersdorf, J., Video-rte nnoscopy using scmos cmerspecific single-molecule locliztion lgorithms, Nt Methods 10(7), (2013). [5] Jnesick, J. R., Photon Trnsfer, SPIE Press Book, (2007). [6] Pertsinidis, A., Zhng, Y., Chu, S., Sunnometre single-molecule locliztion, registrtion nd distnce mesurements, Nture 466(7306), (2010). Proc. of SPIE Vol Z-8

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