Development of a single-photon-counting camera with use of a triple-stacked micro-channel plate

Abstract

At the quantum-mechanical level, all substances (not merely electromagnetic waves such as light and X-rays) exhibit wave–particle duality. Whereas students of radiation science can easily understand the wave nature of electromagnetic waves, the particle (photon) nature may elude them. Therefore, to assist students in understanding the wave–particle duality of electromagnetic waves, we have developed a photon-counting camera that captures single photons in two-dimensional images. As an image intensifier, this camera has a triple-stacked micro-channel plate (MCP) with an amplification factor of 10⁶. The ultra-low light of a single photon entering the camera is first converted to an electron through the photoelectric effect on the photocathode. The electron is intensified by the triple-stacked MCP and then converted to a visible light distribution, which is measured by a high-sensitivity complementary metal oxide semiconductor image sensor. Because it detects individual photons, the photon-counting camera is expected to provide students with a complete understanding of the particle nature of electromagnetic waves. Moreover, it measures ultra-weak light that cannot be detected by ordinary low-sensitivity cameras. Therefore, it is suitable for experimental research on scintillator luminescence, biophoton detection, and similar topics.

Appendix

Figure 10 shows a schematic diagram of the photon-counting camera for estimation of the counting rate. In the figure, the number of photoelectrons emitted from the photocathode per second $x$ (s⁻¹) can be expressed as follows:

$$x = \frac{{I_{\text{pc}} }}{e},$$

(1)

where I _pc and e represent the electric current (A) due to photoelectrons and the elementary electric charge (C), respectively. Here, I _pc is obtained as the product of electric power P (W), energy conversion efficiency of the LED light source η (dimensionless number), total transmittance of four ND filters T (dimensionless number), incidence rate of the light δ (dimensionless number), and the photocathode radiant sensitivity s (A W⁻¹), i.e.,

$$I_{\text{pc}} = \left( {P \ \eta } \right) \ T \ \delta \ s.$$

(2)

Fig. 10

Schematic diagram of the photon-counting camera for estimation of the counting rate. The meaning of each symbol is shown in Table 1

Moreover, P is given by the product of the applied voltage V (V) and electric current I (mA) of the LED light source, and δ is given by

$$\delta = \frac{\psi }{\phi }.$$

(3)

Here, $\psi$ and $\phi$ denote the solid angle (sr) subtended from the LED to the photocathode of the MCP and the solid angle (sr) of the 50 % power angle of the LED:

$$\psi = 2\pi \left[ {1 - \cos \left\{ {{ \arctan }\left( {\frac{2r/2}{d}} \right)} \right\}} \right],$$

(4)

$$\phi = 2\pi \left\{ {1 - \cos \left( {\frac{{\theta_{\text{LED}} }}{2}} \right)} \right\},$$

(5)

where $d$, 2$r$, and $\theta$ _LED denote LED to photocathode distance (mm), the diameter of the effective area of the photocathode surface (mm), and the 50 % power angle (rad) of the LED source, respectively. Finally, x (s⁻¹) is estimated as follows:

$$x = \frac{1}{2e} I \left( {1 - \frac{1}{{\sqrt {1 + \frac{{r^{2} }}{{d^{2} }}} }}} \right) s \ T \ V \ \eta \ { \csc }^{2} \frac{{\theta_{\text{LED}} }}{4}.$$

(6)

Table 1 gives a summary of all parameters.

Table 1 Summary of each parameter and value used in the estimation of the counting rate