# A Method to Obtain the Transducers Impulse Response (TIR) in Photoacoustic Imaging
## 1 Introduction  
As a new imaging method for biological tissues, photoacoustic imaging (PAI) combines the advantages of high contrast in optical imaging and high resolution in ultrasonic imaging. It uses a short-pulse laser as an excitation source to irradiate biological tissue. The optical absorption area inside the sample will undergo isobaric expansion and radiate ultrasonic waves. The acoustic signals resulting from the photoacoustic effect are measured by the use of ultrasonic transducers [1; 2]. In recent years, many new advances have been made in ultrasonic transducers, and they have contributed significantly to developments in the field of PAT [3; 4; 5]. We can reconstruct the spatial distribution of light absorption in a sample using the photoacoustic signals observed by transducers. The spatial distribution of optical absorption inside the sample can be reconstructed from the observed photoacoustic signal (OPAS). PAI provides structural and functional imaging in different application areas, such as vascular imaging [6; 7; 8], brain imaging [9; 10; 11; 12], breast cancer imaging [13; 14; 15; 16; 17], and sentinel lymph node imaging [18; 19; 20; 21]. The resolution of PAI (PAI resolution refers to the sharpness of the image and the amount of information stored in the image) depends on not only the performance of the reconstruction algorithm but also the quality of OPAS. Many reconstruction algorithms usually assume the observation condition is ideal and that the OPAS is the real photoacoustic pressure signal (PAPS) at the transducer positions. However, some factors affect OPAS. Among them, the bandwidth of the transducer is an important one. The TIR of limited bandwidth transducers will deform the waveform of OPAS, and then cause blur in the reconstruction image. TIR is affected not only by the temporal impulse response, but also by the spatial impulse response [22; 23]. To eliminate this effect, [PERSON] applied temporal data deconvolution methods to filter the back-projection algorithm for photoacoustic tomography (PAT) [24]. [PERSON] used the filtered back-projection algorithm for photoacoustic imaging [25]. intravascular PAI [25]. TIR was incorporated into the system matrix to reduce the aroused distortion in the intravascular reconstruction. These studies were conducted under the premise that TIR was known. However, when TIR is unknown, [PERSON] proposed a method combining hybrid weighted adaptive total variation to improve the image quality of PAT [26]. [PERSON] proposed the estimation of the impulse response of photoacoustic systems using homomorphic filtering based on discrete wavelet transform [27]. The proposed method was implemented on experimentally collected photoacoustic data generated from different phantoms and verified through simulation studies with the same photoacoustic targets as the experimental study phantoms. Knowing TIR is the key to eliminating its effect on OPAS. So far, it is usually obtained by experiment measuring. [PERSON] et al., [PERSON], and [PERSON] propose a method to measure TIR by irradiating the transducer with a weak laser pulse [28; 29]. [PERSON] proposed a deconvolution-based PAI reconstruction method [30]. This method deconvolves the OPAS from the point light source with the OPAS from the sample. A projection of the light absorption distribution of the sample can be obtained directly. [PERSON] proposed a method to generate TIR using point-absorbing materials [31]. [PERSON] proposed a PAT image restoration method based on experimentally measured spatially varying TIR to improve image quality and resolution [32]. All the above obtain TIR through experiments. Such measurements not only increase the complexity of the experiment but also make it difficult to ensure experimental accuracy. This paper examines another method for obtaining a TIR for a limited bandwidth transducer. This is a method that does not require any prior knowledge as a known condition to extract TIR directly from OPAS.