The arrangements of the systems are shown in Fig. 1(a). A modulated laser diode was used to generate thermal contraction of the object. To adjust the thermal diffusion length, a computer-controlled signal generator was employed. Fig. 1(b) shows the interaction between the laser and the coarse surface. There were numerous possible paths, including path 1 and 2. Throughout path 1, the interaction between the laser beam and the material occurred only once, which resulted in a normal absorption coefficient (i.e., dielectric function of the Drude model).

Although the electronic interactions were unchanged, the absorption coefficient increased significantly along path 2. This was because the surface geometrical profile captured the light, which led to repeated reflections. A more detailed experiment of this kind was performed in [21], in which the surface roughness level more significantly influenced the absorption coefficient compared to the laser wavelength variation. This conclusion remained consistent even when tested under wider ranges (532–1,064 nm).

Regarding the PA process, this absorption coefficient determined the acoustic initial pressure: p ₀ = Γη _th βF, where Γ, η _th, β, and F are the Gruneisen parameter, energy conversion efficiency, optical absorption coefficient, and laser optical fluence, respectively [22]. Therefore, the PA response on the rough surface was assumed to be insensitive to the laser wavelength variation, and the experiments were conducted using only one wavelength (805 nm, ML520G12; Mitsubishi Electric). A Behringer ECM8000 microphone was utilized to acquire the acoustic waves with a sensitivity of −39.2 dB (11 mV/Pa). The microphone was mounted 10 mm away from the object, forming a 45° angle with the normal line. The collimator lens used was the Mitutoyo Objective Lens BD Plan Apo 7.5×, whose parameters are specified in Table 1.

The tested material was a copper ring with a thickness of 0.05 mm and an outer diameter of 1 mm. The ring lay on the surface of an acrylic printed circuit board. Different object and background materials were chosen to acquire better PA image contrast resulting from different thermal properties. As a comparison, a standard air-couple-based imaging system—namely, the Examet Union 81837 digital microscope (Ogawa Seiki Co. Ltd.)—was used.

According to the RG model, the PA amplitude (Q _PA ) correlates with the thermal diffusion length of the material. Thus, Q _PA specifies the complex envelope of the sinusoidal pressure variation in the form of acoustic magnitude generated by the PA process. For opaque materials (μ _a << l, μ _a << μ _s ), Q _PA is proportional to two states, as follows:

where f, α, and k are laser modulation frequency, diffusivity, and thermal conductivity of the material, respectively [23]. Indices a and s in μ represent air and solid. Afterward, index j is used to represent the order of solid layers. Meanwhile, μ _j and l _j are thermal diffusion length and material thickness, respectively. The first state occurs when the material is under thermally thin conditions (e.g., μ _j > l _j ), whereas the contrary condition is called thermally thick. The two conditions can be achieved by adjusting laser modulation frequency using the following equation:

Eq. (1) shows that the PA amplitude depends on the comparison of the thermal diffusion length and the thickness of the material. Therefore, any alteration of layers can be discovered by gradually varying the modulation frequency. When the modulation frequency satisfies the condition μ _j < l _j , the PA amplitude can be determined by the material at layer j. However, when the frequency is varied until it satisfies the condition μ _j > l _j , the amplitude changes drastically according to the (j + 1)^th layer’s characteristics.

The interaction scheme between the thermal diffusion length and the paint depth is shown in Fig. 2(a). Rough paint was characterized by the thickness of the paint (l _paint ) that enclosed the object surface. According to Eq. (1), three possible conditions existed: μ _paint < l _paint , μ _paint = l _paint , and μ _paint > l _paint . The first condition took place when the paint coat was thicker than its thermal diffusion length and the PA amplitude was determined by the first material layer, Q _PA (μ _paint , k _paint ). When the paint coating layer was thinner than its thermal diffusion length, the third condition was satisfied, and the amplitude became Q _PA (μ _object , k _object ). Theoretically, despite the variation of the paint depth, the PA amplitude did not respond directly. Any alteration occurred only when the paint coat thickness exceeded the threshold of the thermal diffusion length. This became the principal difference between optical and PA imaging due to insensitivity to the surface roughness. The second condition occurred when the paint coat thickness was the same as the thermal diffusion length. Then, the Q _PA experienced a transition from the preceding two conditions.

To run simulations, a number of computations were performed using GNU Octave version 5.1.0 programming. To generate a PA image, Eq. (1) was employed with each associated material parameter. To establish the object, an array was constructed with a dimension of 500 × 500 pixels, on which a copper ring was laid as shown in Fig. 2(b). For simulation purposes, the rough paint was assumed to have a normal distribution with a mean of 2 μm and 3 μm. These values were chosen to approach the thermal diffusion length of the paint, which was 2.46 μm (α _paint = 2.1 × 10⁻⁷ m²/s at modulation frequency of 11 kHz). Thus, the distributions above and below the mean were expectedly balanced.

The PA image resulting from the simulation using these parameters is depicted in Fig. 2(c) for μ _paint > l _paint , where l _paint was the average thickness of the paint. The copper region gave weaker Q _PA in the order of about 0.39 × 10⁻⁹ (a.u). At this state, the shape of the copper ring was displayed clearly because its thermal property significantly affected the Q _PA . Since the thermal conductivity of copper was far different than that of the background (k _copper = 386 W/mK and k _acrylic = 0.40 W/mK), the pixel intensity level could be distinctly discriminated and therefore yielded a higher image contrast.

When l _paint was increased to 3.0 μm, the results changed, as shown in Fig. 2(d). At this state, the condition of μ _paint < l _paint was more likely to happen, and the amplitude Q _PA was dominated only by the paint’s thermal property. Since the thermal conductivity of the paint (k _paint = 1.45 W/mK) was much closer to that of the background (acrylic), the resulting Q _PA parameters were similar in the order of 4.5 × 10⁻⁹ (a.u). Due to this similarity of pixel intensity levels, the image contrast decreased, and the copper ring image became blurred.

Fig. 3(a) shows the object image prior to being coated. By adhering to the prior simulation parameters, a modulation frequency of 11 kHz and a rough paint coating with an average depth of 2.3 μm were used. A commercial acrylic epoxy spray paint (Dull Black-4, RJ London) was applied gradually. The subsequent layer was applied immediately after the previous layer to avoid multilayer coating. After accomplishing the coating process, the average paint depth was measured using the Mitutoyo 193-111 micrometer.

At the initial stage, a single object point was measured, and the signal was recorded for 0.5 seconds. Then, Fourier transformation was performed to obtain the signals spectrum (Fig. 3(b)). Since an open cell configuration was used, the position of the microphone could be arranged to obtain the optimum result. The signal Q _PA was intensely detected with a peak of 11 kHz in accordance with the modulation frequency. The spectrum exhibited a microphone response up to 20 kHz with a background intensity of −70 dB and a peak of up to −57 dB. Due to this large difference, the PA signal could be detected directly.

Prior to measurements, the object image was captured by means of a microscope. The optical pre-coated object image is shown in Fig. 4(a). Visually, the image possessed an excellent quality with high and evenly distributed contrast so that the object shape could be acquired clearly. However, a different result arose for the coated object, as depicted in Fig. 4(b). The rough paint coat created many disturbances in the form of light reflections and randomly distributed high absorbance; as a consequence, the object was barely displayed.

Next, the experiments for PA imaging were conducted using same object. The first scanning result is shown in Fig. 4(d). The PA image showed a high contrast, as was expected from the prior simulation. The object shape was easy to recognize and, accordingly, could be shown as a whole.

Fig. 4(e) shows the PA image of the roughly coated object. Both PA images did not indicate significant changes visually, regardless of the presence of coating. To test this consistency, image subtractions for both modalities were conducted after normalizing each image. The result for the optical images is shown in Fig. 4(c). The inconsistency of the object intensities before and after the coating process were shown; thus, the image subtraction failed to display the object completely. Unlike the optical image, the PA images gave better consistency, and the corresponding image subtraction displayed the real object shape, as shown in Fig. 4(f).

Furthermore, line spread function (LSF) curves were established for all images, as shown in Fig. 4(g) and (h). As indicated before, the optical image had a large change of LSF curves (Fig. 4(g)). Therefore, it could be inferred that the curve widened due to the rough paint coating. The FWHM measurement implied a change of values from 4 μm to 34 μm, giving a consistency of only 12%. The PA images, however, had a smaller change (i.e., from 55 μm to 76 μm), giving a consistency of up to 72%.

The tomography process was carried out by adjusting the penetration depth by changing the value of the thermal diffusion length of the first layer (paint), as given by Eq. (2). In this experiment, four different frequencies were employed: 15.8 kHz, 12.5 kHz, 9.7 kHz, and 1.5 kHz. These corresponded to thermal diffusion lengths of 2.0 μm, 2.6 μm, 9.8 μm, and 52 μm. These frequencies were chosen so that the image slices were distributed to distinct layer depths. Then, the laser beam energy for each modulation was measured using a laser power meter (Sanwa LP1); the results are shown in Table 2.

The resulting tomographic images associated to object depths are shown in Fig. 5(a). When the thickness of the paint coating and copper ring were 2.3 μm and 50 μm, respectively, the image slice for the inner part of the paint coat could be obtained with a modulation of 15.8 kHz (Fig. 5(b)). When the frequency was decreased to 12.5 kHz, the image slice arose from the paint–ring junction, as shown in Fig. 5(c). Since it the image slice was closer to the ring surface, several scratches were seen on the image, as indicated by the arrows in Fig. 5(c). Furthermore, when the frequency was decreased to 9.7 kHz, the middle of the copper ring could be observed (Fig. 5(d)).

At this depth, the copper’s thermal property dominated the establishment of the PA amplitude, as in Eq. (1). Therefore, the resulting image was different from the two preceding images. Compared to the previous images, the intensity of the ring was darker than its background because the thermal conductivity of copper was higher than that of the paint, and the magnitude Q _PA decreased. This transition process also verified that the tomography process occurred at the desired layer. When the frequency was further decreased to 1.5 kHz, the thermal diffusion length of the copper ring surpassed its thickness so that PA imaging produced the base layer image, as shown in Fig. 5(e). At this frequency, the thermally thin condition was satisfied. Therefore, the copper ring became photo-acoustically transparent. In this transparent condition, PA imaging penetrated through the ring and captured the image below it.