Chromatic aberration free reflective mirror-based optical system design for multispectral photoacoustic instruments

1.Introduction

Ultrasound systems have been used for various applications such as diagnosis, sound navigation and ranging, and non-destructive areas [1, 2]. Optical systems have also been applied in biomedical, mechanical, and telecommunication applications [3, 4, 5]. Photoacoustic instruments are combined systems composed of both optical and ultrasound systems. They were recently highlighted for animal and human disease diagnosis because photoacoustic systems utilize the mutual advantages of optical and ultrasound sources [6]. In photoacoustic instruments, optical light rays generated from the optical systems are transmitted to the desired target, to stimulate thermal expansion [7]. The generated thermal expansion can produce acoustic vibrations from the target, and ultrasound transducers can then detect the acoustic signals to obtain the target information [8, 9]. The optical systems can provide higher contrast and lower spatial resolution for organic soft tissues, compared to the use of ultrasound-only systems [10]. Ultrasound systems typically provide lower contrast, and higher spatial resolutions and penetration depths, compared to optical-only systems [11]. For photoacoustic instruments, the light source power is lower than ultrasound power, such that the sensitivities of the photoacoustic instruments are typically lower [8]. Optical sources can provide biological, chemical, and physiological information, such as oxyhemoglobin, deoxyhemoglobin, lipid, melanin, collagen, and elastin information, and ultrasound sources can determine structural information, such as blood vessel wall, fat, and blood velocity [7].

Photoacoustic instruments can be divided into two categories: optical resolution- and acoustic resolution-based photoacoustic instruments [12]. For optical resolution-based photoacoustic instruments, focused ultrasound transducers (either singly or in an array) with mechanical motors are used to scan the organic tissue [13]. For acoustic resolution based-photoacoustic instruments, focused light is used to obtain the target information [7]. The image resolution of optical resolution- and acoustic resolution-based photoacoustic instruments primarily depends on the optical resolution of the optical systems and spatial resolution of the ultrasound transducers [14]. Therefore, optical resolution based-photoacoustic instruments provide higher optical contrast resolution at reduced penetration depths than that of the acoustic resolution based-photoacoustic instruments [15]. However, both photoacoustic instruments need to utilize well-designed optical systems to obtain high quality functional, anatomical, and biological information from the soft tissues of animals and human beings.

Each light used as an optical source has its own limited wavelength range [8]. Therefore, each light can generate different biological tissue information due to different penetration depths. For instance, visible light in the red, green, and blue ranges (between 380 and 740 nm), can be absorbed in certain hemoglobin and melanin in the tissue [8]. The photoacoustic instruments using only a single wavelength light can provide the specific biological tissue data because the protein, melanin, and collagen have different absorption coefficient. Therefore, multispectral photoacoustic instruments were recently implemented to obtain a variety of biological data simultaneously [16, 17, 18]. To utilize multispectral light for obtaining a variety of biological data, photoacoustic instruments have been constructed, either with a variety of combinational structures or with multi optical fibers [16]. However, this method uses the lens to construct the optical system through the refraction of light. In this case, the refractive index of the material used for the lens changes depending on the wavelength. Therefore, when a refractive optical system is used, chromatic aberration is always generated [16, 17]. To reduce the optical chromatic aberrations generated when combining the light beam, the designed convergence structures require detailed optical ray convergence points with proper light power levels [19, 20]. Therefore, we designed novel optical system structures that utilize only one light ray path, to avoid light convergence problems when generating the transmitted light beam for photoacoustic instruments. To the best of our knowledge, we are the first to design a chromatic aberration-free optical system using reflective mirror structures for photoacoustic instruments. The low optical aberration in these optical systems generates low optical resolution for the photoacoustic instruments. In particular, multispectral photoacoustic instruments must generate broad spectral ranges to obtain the desired sample information when combining light of different wavelengths [21, 22]. Therefore, the proposed scheme could be one solution for solving the optical chromatic aberration problems for current multispectral photoacoustic instruments. Section 2 describes the detailed optical design methods of the chromatic aberration-free optical system. Section 3 shows the results and discussion of the designed optical systems and a comparison of the illumination intensity of the combined light beam sources. Section 4 provides concluding remarks.

2.Paraxial design

Optical systems with very narrow field angles, such as telescopes, often consist of only reflective surfaces [23]. However, in the systems, it is very difficult to construct an optical system with only a reflective surface, because the field angle is very wide for photoacoustic instruments [24]. However, optical systems are essentially similar to wide-angle systems, such as in fish-eye optics. The negative-lead type means that the focal length of the first element of the optical system is negative. Such a negative-lead type optical system has a shorter effective focal length (EFL) than back focal length (BFL) and is mainly applied to an optical system with a wide angle of view [25]. Therefore, this optical system must be designed with both a concave and convex mirror. Because the refractive power of the mirror is determined by k=-2/R, the image height and EFL of the optical system consisting of two mirrors are given by Eqs (1) and (2).

where the suffix denotes the surface number, R is the radius of curvature of the mirror, z is the spacing of the surface, and f is the EFL of the optical system.

Here, the total number of unknowns is five; hence, at least three conditions must be provided. In general photoacoustic imaging systems, it is very important to determine the desired target shapes for the optimal mirror and lens, because the chromatic aberration changes rapidly depending on their shapes [26]. However, an optical illumination system is required regardless of the wavelength of the light and the position of the target samples. Therefore, the optical system is initially assumed to be a Cassegrain reflective system, and the shape of the two mirrors is determined as an arbitrary value [27]. In the reflective system, an axial ray at the primary mirror is shielded by the secondary mirror; hence, the primary mirror must be larger than the secondary mirror. Therefore, R1 (the radius of the primary mirror) >R2 (the radius of the secondary mirror) must be satisfied. In this study, R1= 110 mm and R2= 34.5 mm. Suppose that the optical system is designed to exhibit equisolid distortion, and that the field angle range is from 40∘ to 110∘. Further, let us suppose that the image height at 110∘ is 14.5 mm. An instrument body containing an image sensor with a half-diagonal size of 14.5 mm is easily available. Therefore, if the specifications are determined and the optical system is determined, the performance of the optical system can be easily confirmed.

In an optical system with equisolid distortion, the relationship between the field angle θ, the half-diagonal size Y, and the EFL f, is given by Eq. (3).

Under such conditions, the focal length of this optical system is found to be approximately 8.8 mm, and the optical path is shown in Fig. 1.

Figure 1.

Optical layout of paraxial design for wide-angle system.

If designed as shown in Fig. 1, the light source should be placed on the image plane. However, this is not possible due to mechanical interference. Therefore, this must be considered during the design of our relay system. In the relay system, the image formed by the optical system shown in Fig. 1 should be reduced to the size of the light emitting diode (LED). However, if the reduction magnification is high, many mirrors should be used for optical aberration correction. To homogenize the light from the LED, a glass rod with an entrance and exit surface area ratio of four should be used. The most easily available and inexpensive glass rod has an entrance aperture of 6.25 mm2 and an exit aperture of 25 mm2. Positioning the LED in the entrance aperture of the glass rod reduces the numerical aperture (NA) at the exit aperture. In this case, the number of mirrors used in the optical system can be reduced. The half-diagonal size of the glass rod with an exit aperture of 25 mm2 and a square cross section is approximately 3.54 mm. The resulting magnification of the relay system is approximately -0.244 because the image height of the optical system, as shown in Fig. 1, is 14.5 mm. If we suppose the relay system also uses two mirrors, then the axial ray height in the image plane and the magnification would be determined by Eqs (4) and (5).

Figure 2.

Optical layout for relay system.

Figure 3.

Optical layout for coupled system.

Figure 4.

Ray fan of our optimized system.

Figure 5.

3D optical layout for our optimized system.

Figure 6.

Intensity distribution and normalized intensity profile.

In Eqs (4) and (5), m is the magnification and m=-0.244. Therefore, there are five unknowns, and three additional conditions must be provided. The distance between the mirrors will be approximately determined. Assuming that the distance z3 from the image surface of the optical system to the first mirror of the relay system is 90 mm, the distance z4 between the two mirrors is 50 mm, and the distance z5 from the last mirror to the image surface is 160 mm, and R3= 30.06 and R4= 90.992 are obtained. The optical layout of the relay system is shown in Fig. 2. Therefore, a paraxial design can be obtained by combining two designed optical systems.

3.Results and discussion

4.Conclusion

A chromatic aberration-free optical system using reflective mirrors was designed for multispectral photoacoustic instruments. The LED light sources are cost-effective and relatively safe compared to the traditional laser light sources used in photoacoustic instruments. Therefore, the photoacoustic instruments using LED light sources have been designed. Because different wavelengths are needed for different tissue characterization, multi-spectral photoacoustic instruments have been developed. However, the currently developed multispectral photoacoustic instruments have high chromatic aberrations, thus deteriorating optical resolution. Therefore, we developed a new type of multispectral optical design using a reflective mirror instead of the refracted optical lens used in conventional systems. Because we constructed a system with only a reflective surface, an aberration-free optical system was achieved. These results were confirmed from aberration plots and a normalized intensity profile. In the optical design, the intensity distribution at a position 150 mm away from the optical axis in the vertical direction exhibited adequate light intensity values. Therefore, the developed chromatic aberration-free optical system using a reflective mirror is a potential candidate for use in multispectral photoacoustic instruments.