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Development of a Time-Integration Method for Analyzing the Photoresponse of Image Sensors: Theoretical and Experimental Verification with Digital Cameras Cover

Development of a Time-Integration Method for Analyzing the Photoresponse of Image Sensors: Theoretical and Experimental Verification with Digital Cameras

Measurement Science Review
Volume 26 (2026): Issue 2 (April 2026)
By: Nobuaki Shimoji and  Yuto Suzuki  
Open Access
|Mar 2026

Figures & Tables

Fig. 1.

Schematic of a single four-transistor pixel in a CMOS image sensor based on an active pixel sensor design. The pixel includes a pinned photodiode (PPD), a transfer gate (TG), a floating diffusion (FD), a reset transistor (Rst), a source follower amplifier (SFA), and a row select transistor (RS). An on-chip microlens and an on-chip color filter are positioned above the PPD.

Fig. 2.

(a) Lightning impulse voltage waveform (e.g., Fig. 2.23, Chapter 2 [28]), and (b) illustration of the wavefront of the lightning impulse voltage (solid line) approximated by sinusoidal light (dashed line) as indicated by the radiant flux Φe. The front time T1 is 1.2 μs, and the time-to-half-value T2 is 50 μs. Both T1 and T2 start from the virtual origin O1. The period of the sinusoidal light is denoted by Tsin. The lightning impulse voltage and radiant flux Φe are normalized, with their maximum values expressed as unity, respectively.

Fig. 3.

(a) Light signal (Fig. 2 [29]) and (b) current waveform (Fig. 4 [30]) of lightning. The 10/90 rise time of the light signal is approximately 1.15 μs, and that of the current is approximately 1.13 μs. Since a strong correlation between current and light intensity has been shown up to the peak of the lightning current, the current waveform up to the peak can be directly interpreted as the light intensity [29].

Fig. 4.

Radiant flux Φe (t) vs. time t. (a) The radiant flux ΦeDC \Phi _{\rm{e}}^{{\rm{DC}}} of constant brightness light remains constant with respect to t, and its radiant energy QeDC Q_{\rm{e}}^{{\rm{DC}}} is represented by the dotted (green) region. (b) Φe,1sint \Phi _{{\rm{e}},1}^{\sin}\left( t \right) is a sinusoidal wave with frequency f1. The period of Φe,1sin \Phi _{{\rm{e}},1}^{\sin } is T1sin T_1^{\sin } , and during the exposure time texp, there are n1 periods. The difference between texp and n1T1sin {n_1}T_1^{\sin } is the residual tr,1. (c) Intuitive illustration of the integral of Φe,1sint \Phi _{{\rm{e}},1}^{\sin }\left( t \right) , where the radiant energy Qe,1sin Q_{{\rm{e}},1}^{\sin } of the sinusoidal light Φe:1sin \Phi _{{{\rm{e}}_:}1}^{\sin } is approximately equal to Q1DC Q_1^{{\rm{DC}}} , since the residual Qe,1res Q_{{\rm{e}},1}^{{\rm{res}}} indicated by the upper part of the diagonal stripe region is smaller than Qe,1sin Q_{{\rm{e}},1}^{\sin } . (d) Φe,2sint \Phi _{{\rm{e}},2}^{\sin }\left( t \right) is the sinusoidal light with frequency f2, where f2 > f1. Since the frequency f2 is greater than f1, the period T2sin T_2^{\sin } is shorter than T1sin T_1^{\sin } , and the number of waves n2 within the exposure time texp is greater than n1. Moreover, the residual radiant energy approaches zero as the frequency increases.

Fig. 5.

Digital cameras and lenses used: (a) CamC, (b) CamN, (c) CamP, (d) Cf18-55, (e) Nf18-55, and (f) Pf12-32.

Fig. 6.

(a) Front view of the integrating sphere used in the study, and (b) reflectance ρ of the white pigment coating the interior of the integrating sphere.

Fig. 7.

Schematic circuit diagram of the sinusoidal light source. To minimize noise, the LED driver is housed in a metal aluminum shielded box, while the light-emitting component is placed inside an aluminum mesh box. The sinusoidal wave (peak voltage Vp = 0.5 V, peak-to-peak voltage Vpp = 1 V) from the oscillator and the bias voltage (Vbias = 0.5 V) from the constant voltage circuit are input to the summing amplifier.

Fig. 8.

Schematic circuit diagram of the photosensor. Due to the small photocurrent IP (in the range of several tens of microamperes), the output voltage VP is amplified by a factor of 3.3 using the non-inverting amplifier, with the voltage across the shunt resistor R2 serving as the input.

Fig. 9.

Central 4 × 4 pixels of the RAW data in Bayer format. This region includes 4 pixels for the blue (B) channel, 8 pixels for the green (G) channel, and 4 pixels for the red (R) channel.

Fig. 10.

(a) Setup of the camera and integrating sphere, and (b) arrangement of each measurement module. The positioning of each module is as follows: (i) integrating sphere, (ii) digital camera, (iii) and (iv) DC-stabilized power supply, (v) oscillator, (vi) LED driver, (vii) photosensor, and (viii) oscilloscope. To shield ambient light, the integrating sphere and camera were covered with a black plastic sheet during photography.

Fig. 11.

Output waveforms of the sinusoidal light source and photosensor at frequencies of (a) 10 Hz and (b) 1 MHz.

Fig. 12.

Pixel value V versus frequency f, absolute error Eabs versus frequency f, and relative error Erel versus frequency f for (a) CamC, (b) CamN, and (c) CamP. The results for the B, G, and R channels are presented from left to right. The solid and dashed horizontal lines represent the DC pixel value VDC and the mean pixel value, respectively.

Cameras and lenses used, along with their corresponding symbols_ In subsequent sections, each camera and lens is represented by the symbols listed in the Symbol column_

Camera/LensManufacturerProduct nameSymbol
CameraCanonEOS 9000DCamC
CameraNikonD5600CamN
CameraPanasonicLumix DC-GF10WCamP
LensCanonEF-S18-55mm F4-5.6 IS STMCf18-55
LensNikonAF-P DX NIKKOR 18-55mm f/3.5-5.6G VRNf18-55
LensPanasonicLumix G VARIO 12-32mm/F3.5-5.6 ASPH./MEGA O.I.S.Pf12-32

Dark values of the image sensors in three cameras_

CameraBGR
CamC2045.902045.282045.72
CamN2408.162406.072408.68
CamP2288.02282.02284.0

Electronic components in the LED driver and photosensor_ The physical quantities listed include: bias current and slew rate of the operational amplifier (IB and SR), rise and fall times of the MOSFET (tr and tf), zener voltage (VZ), luminous intensity (IV), forward current of the LED (IF), photocurrent of the photodiode (IP), and illuminance (EV)_

CircuitPart symbolPart nameManufacturerProduct numberDescription
LED driverOpAmpOperational amplifierNisshinbo Micro DevicesNJM2742DIB = 80 nA, SR= 10 μs
LED driverN-ch MOSFETMOSFETMicrochip TechnologyDN2540N3-Gtr = 15 ns, tf = 20 ns
LED driverZDZener diodeNexperiaBZX79-C5V1,113VZ = 5.1 V
LED driverLEDWhite LEDCree LEDC503D-WAN-CCbEb151Iv = 40 cd, IF = 20 mA
LED driverRed LEDRed LEDDiCUNO–Red, Iv = 3 cd, IF = 20 mA
LED driverCoaxial cableCoaxial cable–RG174BNC terminated, 1.5 m, 50 Ω
PhotosensorOpAmpOperational amplifierNisshinbo Micro DevicesNJM072BD (discontinued)IB = 13 pA, SR = 13 μs
PhotosensorPDPhotodiodeams-OSRAMBPW 34IP ≥ 55 μA, EV = 1000 lx
PhotosensorE1Ni-MH rechargeable batteryRS Pro199-6468.4 V, capacity 200 mAh

Camera settings for photography_ Brightness information is influenced by the exposure time t, ISO gain, focal length f, and F-number F/#_ The exposure time and ISO gain are directly related to the image sensors, while the focal length and F-number pertain to the lenses used_

CombinationCameraLens
Camera-Lenst (s)ISOf (mm)F/#
CamC-Cf18-551100184
CamN-NCf18-551100184
CamP-Pf12-321/2200134
DOI: https://doi.org/10.2478/msr-2026-0007 | Journal eISSN: 1335-8871
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Language: English
Page range: 46 - 56
Submitted on: Feb 20, 2025
|
Accepted on: Jan 12, 2026
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Published on: Mar 4, 2026
Published by: Slovak Academy of Sciences, Institute of Measurement Science
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open
Keywords:
digital camera,
image sensor,
photoresponse,
frequency dependence,
photometry,
sinusoidal light
Related subjects:
Engineering,
Electrical engineering,
Control engineering, metrology and testing

© 2026 Nobuaki Shimoji, Yuto Suzuki, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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