To meet the imaging requirements of high resolution and large field-of-view, infrared target detection optical systems should utilize complex optical lens groups, which results in large volume, weight, and total system length. As a result, they are not suitable for deployment on optical payload platforms with limited space, such as airborne and spaceborne platforms. The infrared fiber image bundle is soft and easy to bend, and adding this kind of bundle to the traditional optical system can flexibly change the optical path and shorten the overall length of the system. However, infrared fiber image bundle optical systems have the nature of spatially double discrete sampling effect, and their imaging characteristics are different from those of traditional optical systems. This makes the traditional target detection signal-to-noise ratio (SNR) formula applicable to linear space-invariant systems and no longer applicable to infrared fiber image bundle optical systems. To this end, we present an innovative method for quantitatively analyzing the target detection capability of infrared fiber image bundle optical systems. The proposed method adopts statistical analysis to complete the derivation of the target SNR and the SNR attenuation coefficient formulas, featuring clarity, simplicity, and easy calculation. We hope that this method will contribute to the optical design, device selection, and system detection capability analysis of infrared fiber image bundle optical systems.

The target detection scenario of infrared fiber bundle optical systems is set to detect distant point targets under a uniform background in the sky. Thus, the signal and noise components are appropriately corrected respectively to obtain the target detection SNR formula of these systems. First, the overall transmittance of infrared fiber bundle optical systems is obtained by combining the product of the fiber transmittance and the fiber bundle filling factor, the transmittance of the front telescopic system, and the transmittance of the rear coupling system. Then, the proportion of the cross area between the core area of the fiber bundle and the photosensitive area of the detector pixel is defined as the system filling factor, which is employed to characterize the spatially double discrete sampling effect. By utilizing the overall transmittance and filling factor of optical systems, the noise equivalent temperature difference can be statistically derived, and then the noise equivalent power can be obtained, which represents the noise component of infrared fiber bundle optical systems. For the signal component correction, the introduction of the pulse visibility factor is to describe the energy concentration of infrared fiber bundle optical systems on the point target image. Based on the correction formulas for the above-mentioned noise and signal components, a target SNR formula for infrared fiber bundle optical systems is derived, which includes target radiation characteristics, background radiation characteristics, optical system parameters, and detector parameters. To simplify the analysis of system detection capability, we define the SNR attenuation coefficient as the proportion of SNR decrease in infrared fiber bundle optical systems compared to traditional optical systems. Finally, combined with the derived SNR attenuation coefficient and designed structural parameters of the infrared fiber bundle optical system, the system filling factor and pulse visibility factor are calculated, and the relationship between the fiber transmittance and the SNR attenuation coefficient is given. Finally, this can quantitatively evaluate the difference in the detection ability of the infrared fiber bundle optical system.

In the condition of vertical coupling alignment assembly (or matching a certain column of vertical fiber bundle images with a square pixel line array), we combine the optical design results of the point spread function (PSF) of the front telescopic system and the rear coupling system (Fig. 8), and the fiber bundle characteristic function distribution (Fig. 9). Meanwhile, the average pulse visibility factor of the infrared fiber bundle optical system with the fiber bundle resolution of 25×256 toward the point target is calculated to be 0.1335. Due to the coupling mismatch between the infrared fiber bundle and the square pixel array, the fiber coupling area varies for different pixels (Fig. 13), with the calculated average filling factor of 0.4201. Based on the calculated pulse visibility factor and system filling factor of the infrared fiber bundle optical system and the traditional optical system, the relationship between the detection SNR attenuation coefficient ASNR and the fiber transmittance τfiber is given (Fig. 14), and the following conclusions can be drawn. Under τfiber>0.9, ASNR<0.5; under τfiber<0.3, ASNR>0.7; under τfiber<0.03, ASNR>0.9. Therefore, it is advisable to adopt fiber bundle devices with high transmittance to improve the detection capability of fiber bundle systems.

We propose an innovative quantitative analysis method for the ability of infrared fiber bundle optical systems to detect distant targets, thereby solving the problem that traditional target SNR formulas are not applicable to such optical systems with spatially double discrete sampling effect. Based on the imaging theory of infrared fiber bundle optical systems, the target SNR formula is derived by appropriately modifying the signal expression and noise expression. Additionally, the SNR attenuation coefficient expression of the system compared to traditional optical systems is provided, which can effectively characterize the detection ability of the system. Based on the designed infrared fiber bundle optical system, key performance parameters such as the pulse visibility factor and system filling factor are simulated and calculated. The relationship between the fiber transmittance and SNR attenuation coefficient is further analyzed, with the detection ability differences between the two types of optical systems quantitatively compared. The simulation results demonstrate the influence of the spatially double discrete sampling effect on the infrared fiber bundle optical system and clarify that the SNR attenuation coefficient is related to a fixed coefficient of 0.5459 and fiber transmittance. Thus, it is indicated that the detection capability of the system can be improved by selecting fiber bundle devices with high transmittance. Finally, we can provide a theoretical basis for determining the detection ability boundary of infrared fiber bundle optical systems.