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

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/Lens	Manufacturer	Product name	Symbol
Camera	Canon	EOS 9000D	CamC
Camera	Nikon	D5600	CamN
Camera	Panasonic	Lumix DC-GF10W	CamP
Lens	Canon	EF-S18-55mm F4-5.6 IS STM	Cf18-55
Lens	Nikon	AF-P DX NIKKOR 18-55mm f/3.5-5.6G VR	Nf18-55
Lens	Panasonic	Lumix G VARIO 12-32mm/F3.5-5.6 ASPH./MEGA O.I.S.	Pf12-32

(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 Φ_e. 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 T^sin. The lightning impulse voltage and radiant flux Φ_e are normalized, with their maximum values expressed as unity, respectively.

(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].

Radiant flux Φ_e (t) vs. time t. (a) The radiant flux $Φ_{e}^{DC}$ of constant brightness light remains constant with respect to t, and its radiant energy $Q_{e}^{DC}$ is represented by the dotted (green) region. (b) $Φ_{e, 1}^{sin} (t)$ is a sinusoidal wave with frequency f₁. The period of $Φ_{e, 1}^{sin}$ is $T_{1}^{sin}$ , and during the exposure time t_exp, there are n₁ periods. The difference between t_exp and $n_{1} T_{1}^{sin}$ is the residual t_r,1. (c) Intuitive illustration of the integral of $Φ_{e, 1}^{sin} (t)$ , where the radiant energy $Q_{e, 1}^{sin}$ of the sinusoidal light $Φ_{e_{:} 1}^{sin}$ is approximately equal to $Q_{1}^{DC}$ , since the residual $Q_{e, 1}^{res}$ indicated by the upper part of the diagonal stripe region is smaller than $Q_{e, 1}^{sin}$ . (d) $Φ_{e, 2}^{sin} (t)$ is the sinusoidal light with frequency f₂, where f₂ > f₁. Since the frequency f₂ is greater than f₁, the period $T_{2}^{sin}$ is shorter than $T_{1}^{sin}$ , and the number of waves n₂ within the exposure time t_exp is greater than n₁. Moreover, the residual radiant energy approaches zero as the frequency increases.

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

(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.

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 V_p = 0.5 V, peak-to-peak voltage V_pp = 1 V) from the oscillator and the bias voltage (V_bias = 0.5 V) from the constant voltage circuit are input to the summing amplifier.

Schematic circuit diagram of the photosensor. Due to the small photocurrent I_P (in the range of several tens of microamperes), the output voltage V_P 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.

Table 2.

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.

Combination	Camera		Lens
Camera-Lens	t (s)	ISO	f (mm)	F/#
CamC-Cf18-55	1	100	18	4
CamN-NCf18-55	1	100	18	4
CamP-Pf12-32	1/2	200	13	4

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.

(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.

Table 3.

Dark values of the image sensors in three cameras.

Camera	B	G	R
CamC	2045.90	2045.28	2045.72
CamN	2408.16	2406.07	2408.68
CamP	2288.0	2282.0	2284.0

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

Pixel value V versus frequency f, absolute error E_abs versus frequency f, and relative error E_rel 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 V_DC and the mean pixel value, respectively.

Table 4.

Electronic components in the LED driver and photosensor. The physical quantities listed include: bias current and slew rate of the operational amplifier (I_B and SR), rise and fall times of the MOSFET (t_r and t_f), zener voltage (V_Z), luminous intensity (I_V), forward current of the LED (I_F), photocurrent of the photodiode (I_P), and illuminance (E_V).

Circuit	Part symbol	Part name	Manufacturer	Product number	Description
LED driver	OpAmp	Operational amplifier	Nisshinbo Micro Devices	NJM2742D	I_B = 80 nA, SR= 10 μs
LED driver	N-ch MOSFET	MOSFET	Microchip Technology	DN2540N3-G	t_r = 15 ns, t_f = 20 ns
LED driver	ZD	Zener diode	Nexperia	BZX79-C5V1,113	V_Z = 5.1 V
LED driver	LED	White LED	Cree LED	C503D-WAN-CCbEb151	I_v = 40 cd, I_F = 20 mA
LED driver	Red LED	Red LED	DiCUNO	–	Red, I_v = 3 cd, I_F = 20 mA
LED driver	Coaxial cable	Coaxial cable	–	RG174	BNC terminated, 1.5 m, 50 Ω
Photosensor	OpAmp	Operational amplifier	Nisshinbo Micro Devices	NJM072BD (discontinued)	I_B = 13 pA, SR = 13 μs
Photosensor	PD	Photodiode	ams-OSRAM	BPW 34	I_P ≥ 55 μA, E_V = 1000 lx
Photosensor	E₁	Ni-MH rechargeable battery	RS Pro	199-646	8.4 V, capacity 200 mAh

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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

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.

Volume 26 (2026): Issue 2 (April 2026)

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

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Table 4.

Paradigm

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