Medical ultrasound (acoustic) systems have long been used to assess tissues in the human body [1-3]. Acoustic signals generated by medical ultrasonic (ultrasound) transducers are delivered to tissues and reflected echo signals are detected by transducers to monitor the properties of biological tissues [4]. The spatial resolution of an ultrasound system is mainly determined by the transducer [5, 6] and penetration depth must be sacrificed for better spatial resolution.

Opto-acoustic systems are relatively expensive and less portable hybrid techniques compared to conventional ultrasound-only systems [7, 8]. Nonetheless, opto-acoustic systems have been used in order to detect gas and chemical components or to obtain anatomical and molecular properties of biological tissues, because of the high contrast and spatial resolution provided by the advantages of utilizing light and ultrasound [8]. Compared to medical ultrasound systems, opto-acoustic systems utilize excitation sources such as light because of the high contrast provided by the optical sources [8]. Pulsed or continuous sources are delivered to the tissues through optical fibers or lenses, generating rapid thermal expansion, which leads to the formation of acoustic signals and then, reflected echo signals produced by the thermal expansion are detected by ultrasound detectors [9, 10]. The ultrasound receiver then processes the data using a PC [11].

Recently, there have been remarkable developments in optical measurement techniques to diagnose ocular tissues [12, 13]. Laser technology is at present the standard method in the field of ophthalmology because of its ability to provide high contrast and resolution of the retina [14]. The intensity of the high-power light sources needs to be accurately controlled in order to avoid damage to living tissues in the eye [15]. Compared to lasers, light emitting diodes (LEDs) are relatively low cost and compact excitation optical sources [16, 17]. In order to use LED sources in such systems, specialized lenses need to be designed and characterized in order to detect the tissues from depth greater than 3 cm from the anterior surface of the eye areas, because LEDs are normally divergent light sources. Proper lens design is necessary because properly powering LED sources helps to effectively yield acoustic signals with adequate amplitudes while the use of commercial off-the-shelf lenses would require extensive tests to characterize the light source. Additionally, pulsed LED light is proposed for our developed light emitting diode-acoustic (LEDA) system because pulsed laser light signals can provide higher signal-to-noise ratio (SNR) than continuous laser light signals [18]. In this manuscript, we describe the feasibility of LEDA systems using pulsed power LED sources with a custom designed Ramsden eyepiece lens for ophthalmology applications by using bovine and big-eye tuna eyes.

Divergent LED light needs to be focused through a lens in order to obtain information about tissues in specific areas of the eye. Assuming that light generated from the LED is a collimated beam illuminating an area with a diameter of 20 mm (a typical size of the pupil of the eye), a singlet - which is a lens consisting of a single simple element - can be located in front of the LED for focusing. However, if the light source area is so large as to produce non-uniform intensity distribution of the light, then several lenses need to be utilized to satisfy the telecentric condition that the chief ray is at zero angle of incidence. In this study, only two identical lenses are needed to construct a Ramsden eyepiece type optical lens in order to reduce the fabrication cost. As shown in Fig. 1, a Ramsden eyepiece is a kind of loupe type lens which satisfies the purpose of our research. This system consists of two plano-convex lenses, where one surface of each lens is flat. This lens can be useful if an LED with single wavelength is utilized and if a white LED with chromatic aberration is not considered. Figure 1 illustrates the optical layout of the Ramsden eyepiece designed for our study.

Before we calculate the shape, such as the curvature and thickness of the lens, the refracting power needs to be determined. Two identical plano-convex lenses are used, and thus the refracting power of each lens needs to be equal. The distance between the lens and LED is much larger than the thickness of the lens, and thus here we neglect the thickness of the lens. If we can assume that the optical lens consists of two thin lenses, then the axial ray and chief rays in the optical lens could be illustrated as in Fig. 2.

In Fig. 2, we describe the axial ray and chief ray path designed in the optical lens. The illumination area is the zero-th surface and the LED light source is the third surface. Ray-tracing of the chief ray and paraxial ray with Gaussian bracket and matrix are expressed in Eqs. (1) and (2) [19, 20].

Here, u₀ is assumed to be zero if the illuminating area is constant according to the distance variation from the LED light source. Additionally, the paraxial angle of the chief ray () is assumed to be zero in the LED in order to satisfy the telecentric condition which represents that the light intensity needs to be constant with respect to the LED size. In order to transfer the maximum lighting power from the LED to the illuminating area, the numerical aperture (NA) in the optical lens should be as large as possible. The practical limitation of the NA also needs to be considered if the optical lens consists of two identical lenses.

The divergence angle of a light beam generated from the LED was set to be ±30°. This value implies that the light generated from the LED can approach the pupil (illumination area) with ±30° angle of the view. In order to satisfy this condition, the NA of the optical lens was calculated as 0.5 (= sin 30°). The relationship between the NA and f-number (F/#) can be represented in Eq. (3) [21]. Using Eq. (3), the calculated F/# is 2.0. Therefore, the effective focal length (EFL) is 40 mm because the diameter of the pupil in the optical lens is 20 mm.

The distance between the second lens and LED is set to be more than 25 mm. The EFL can be derived using the Gaussian bracket in Eq. (4) [19].

Using Eqs. (1) and (2), the distance between the illuminating area and the first lens (d₀) is equal to the distance between the second lens and the LED (d₂) if Eqs. (5) and (6) need to be satisfied because of the symmetry of the designed optical lens.

Using the property of the Gaussian bracket, Eq. (7) could be solved when Eq. (4) is substituted into Eq. (6). If we assume the distance between the second lens and the LED (d₂) is 2.5 cm, the distance between the first lens and the second lens (d₁) can be calculated. The refracting power can be calculated using Eq. (7) because two identical lenses are used, thus using the condition as k₂ = k₁

If Eq. (4) is substituted into Eq. (7) and the symbols related with the distance d₁ between the two lenses are removed, Eq. (8) related to the refracting power k₁ can be obtained. Then, Eq. (8) is substituted into Eq. (7), and the distance d₁ between the two lenses can be obtained. In Eqs. (8) and (9), n₀ is the refractive index in the illuminating area and n₁ is the refractive index in the space between the two lenses. If the two lenses are located in air, the refractive index of the illuminating area is n₁ = 1.

Based on the given condition above, we can obtain k₁ = 1/65 mm^-1 and d₁ = 40 mm. If the focal length of the lens is the reciprocal of the refracting power, the focal length of the two lenses is 65 mm.

If we determine the focal length of each lens, we need to define the lens shape, which is given by the curvatures of the front and rear surfaces of the lens. As shown in Fig. 1, the optical ray path indicates that the ray collimated in parallel with the pupil is focused on a certain spot. Therefore, the focal length of the singlet with zero magnification is 65 mm, and we thus obtain the curvature of the front and rear surfaces of the lens if the spherical aberration is minimal. The spherical aberration can be calculated using Eq. (10) [22]. In Eq. (10), Y takes fixed values such that we can find X if S_I is the minimal.

where h is the height of the axial ray from the front surface of the lens, k₁ is the refracting power of the lens, n is the refractive index of the lens material, m is the magnification of the lens, c₁ is the curvature of the front surface of the lens and c₂ is the curvature of the rear surface of the lens, and the spherical aberration S_I cannot be zero for a singlet.

The refracting power of a thin lens can also be expressed by the curvature and refractive index as Eq. (11) as below

Therefore, the curvature in the front and rear surfaces of the lens c₁ and c₂ can be calculated if the calculated X called the form factor in Eq. (10) is substituted into Eq. (11). The lens material needs to be selected to have low refractive index variance at different wavelengths. For example, the refractive index of the He yellow d-line with 58.76 cm is 1.48749 for the relatively cheap optical glass FC5 produced from the HOYA company [23, 24]. However, the calculated thickness of this kind of lens is zero such that the fabrication of this lens is not possible. Therefore, we need to define the proper thickness of the lens. However, the spherical aberration S_I and refracting power k₁ need to be changed if the thickness of the lens is considered. With a certain lens thickness, the original spherical aberration SI and refracting power k₁ need to be constant if we use the equivalent lens method [25]. However, using this method, the aberration of the entire total optical lens cannot be minimized even if the aberration of the first lens is minimized. Therefore, the lens shape can be determined when we select the thickness of the lens with the optimization function in the optical design software. Figure 3 shows the result of using the imaging optics design software (CodeV, Synopsys, Mountain View, CA, USA). In Fig. 3, the “Radius” represents the specific value to describe the characteristics of the lens shape, which is the reciprocal of the curvature. The data in Fig. 3 are extracted from the optical layout in Fig. 1.

The focal length of the optical lens is related to the efficiency of the optical lens as shown in Eq. (3), such that the initially designed value of the focal length of the optical lens was supposed to be 40 mm. However, the focal length of each lens may not be a problem if aberration is minimized even when the initial value is different. If we calculate using the data in Fig. 3, the focal length is 70.604 mm.

Figure 4 illustrates how an optical ray can be focused on the LED surface if the ray bundle starts in the pupil surface as shown in Fig. 1. Figure 4 shows a spot diagram of the designed optical lens. The high performance of the optical lens is indicated by the fact that the ray bundle is well focused in one spot and the spot size is supposed to be small. As shown in Fig. 4, the spot variance is not high if the image plane moves back and forth by 0.5 mm or if the LED locations move by a few millimeters. The operating condition of the optical lens is to visualize the sample such that the LED light is a collimated beam generated from the optical lens. Therefore, the illumination area is not changed significantly even if the LED shifts back and forth (back/forth) or moves up and down (up/down), and we confirm that the optical lens is well designed for the purpose of the experiment.

As previously described, the expected performances of the designed optical lens was simulated and characterized because the light distribution and intensity after transmitting the custom-made lens need to be verified before integrating into the LEDA systems for ophthalmology applications. As the lens shape was determined, the intensity profile of the light on the illuminating area was calculated at different LED locations. As shown in Fig. 5, a 3D optical layout was input to illumination optics design package, LightTools (LightTools, Synopsys, Mountain View, CA, USA). In this design, the light generated from the LED passes through the pupil.

Figure 6 illustrates the illuminance distribution profiles vs. LED wavelength when the LED was located in the center of the ideal optical lens without any aberration. Additionally, the peak wavelengths and power of the LED with 628 nm, 524 nm and 460 nm wavelengths and 0.3 W power was modeled based on red, green, and blue LEDs (CBT-120, Luminus Devices, Sunnyvale, CA, USA). As shown in Fig. 6, the optical lens with these LED lights are guaranteed to cover the sample, which has 2 cm diameter. The light intensity is almost constant across the entire illumination area.

Figure 7 illustrates the profile of the illuminating light intensity. The light intensities of these LEDs are supposed to vary as the applied current to the LEDs changes, in accordance with the luminance properties of the LEDs. According to the performance verification, the light intensities of the 628 nm, 524 nm, and 460 nm LEDs at the center of the illumination field are 0.057 mW, 0.071 mW, and 0.121 mW, respectively.

The illumination profile of the light need to be confirmed, due to possible errors during fabrication and assembly. Generally, manufacturing errors are not significant; however, there may be relatively large errors in the LED assembly location and the sample location in the measurement. Generally, the optical lens and its fixture components need to be fairly precisely assembled. Therefore, we only analyzed the errors caused by the back/forth and up/down motion of the LEDs at the optical axis, and the up/down motion of the samples. The illuminating intensity profile of the light using these variances is plotted in Fig. 8. In Fig. 8, the wavelength of the LED is assumed to be 524 nm.

As shown in Fig. 8, the light intensity profiles do not change significantly with sample movement. Additionally, we could obtain the same light intensity profiles even if the LED wavelength changed.

Figure 9 shows the experimental pulse-echo response setup of the LEDA systems in order to demonstrate the capability of the system; pulse-echo response is one of the traditional methods to measure the length of the eye and estimation of the eye lens power, which in turn provide information regarding eye disorders and diseases [26]. Opto-acoustic applications typically utilize visible and near-infrared light spectrum ranges (400-1800 nm) [8, 27, 28] and visible light spectrum in the eye are essentially between 400 nm and 700 nm wavelength ranges. We therefore selected red, green, and blue LEDs with 450-470 nm, 510-540 nm and 611-631 nm wavelengths (CBT-120, Luminus Devices, Sunnyvale, CA, USA), respectively. The retina in the bovine eye has photoreceptor cells which sense typically three different light colors (blue, green, and red) filters such that the light emitting source between 479 and 512 nm was also selected for the bovine eye [12]. Moreover, in order to avoid possible damage to the eye, the high power LED sources should be used with proper pulse repetition frequency (PRF = 1 kHz) or duty cycles. Therefore, each LED, which is mounted on the driver (EL-5502, Luminus) and controlled by a power supply (E3631A, Agilent Technologies, Santa Clara, CA, USA) and function generator (AFG3252, Tektronix Inc., Beaverton, OR, USA), was emitted through designed Ramsden eyepiece to the eye samples. Upon illumination, the reflected echo signal was detected by a 10 MHz transducer (V311-SU, Olympus Corporation, Tokyo, Japan). The transducer was immersed in a water bath at a depth of 3 cm. The echo waveform was amplified by a 40 dB preamplifier (AU-1114, MITEQ, Hauppauge, NY, USA) and then displayed by an oscilloscope (MSO2024B, Tecktronics, Beaverton, OR, USA) before processing the data using MATLAB program (MathWorks, Natick, MA, USA) in the PC in order to plot the waveform in the time and frequency domains. Figure 9(b) shows the measurement setup with bovine eye in the bath.

Figure 10 shows the echo waveforms and their spectrum data using red, green, and blue LED lights acquired from the bovine eye. The received echo amplitudes of the transducers with the red, green, and blue LEDs are 3.84 mV, and 3.92 mV, and 5.49 mV, respectively. These amplitude data confirmed that the different echo amplitudes could be obtained depending on the light intensity profiles obtained in Fig. 7. The first echo signal response times of the red, green, and blue LEDs are 20.27 µs, 20.33 µs, and 20.94 µs, respectively. Therefore, the calculated distances from the transducer using red, green, and blue LEDs are 31.2 mm, 31.3 mm, and 32.2 mm, respectively. The center frequencies of the red, green and blue LEDs, with the −6 dB bandwidths in parentheses, are 9.81 MHz (8.35%), 10.09 MHz (10.01%), and 10.45 MHz (16.26%), respectively. These experimental results demonstrate the detection capability of the developed LEDA system, which can achieve high penetration depths in the bovine eyes with different LED intensities and visible light wavelengths. These results indicate that the developed ophthalmology pulse-echo measurement system could detect the echo waveform in the eye area.

Figure 11 shows the experimental setup of the pulse-echo response with the bigeye tuna eye in order to demonstrate the capability of the high frequency (>15 MHz) ultrasound transducers as high frequency ultrasound transducers can provide higher spatial resolutions at the expense of tissue penetration depth, and spatial resolutions are proportional to the bandwidth of the echo signals. In this experiment, we also selected the same red, green, and blue LEDs (CBT-120, Luminus Devices), respectively. Each LED which is also controlled by the LED control driver (EL-5502, Luminus), a power supply (PAS20-36, Kikusui Electronics Corp., Yokohama, Japan) and function generator (AFG3252) was emitted through designed Ramsden eyepiece to the eye. Upon illumination, the reflected echo signal was detected by a 25 MHz ultrasound transducer (V324-SU-F3.00IN-PTF, Olympus Corporation, Tokyo, Japan). The ultrasound transducer was immersed in a water bath at a depth of 6 cm depth along the focal point of the transducer. The echo waveform was amplified by a 65 dB preamplifier (AU-1525, NARDA-MITEQ Inc., Hauppauge, NY, USA) followed by the 20 dB active low pass Sallen-Key filter with 120 MHz cut-off frequency and then displayed on an oscilloscope (MSO2024B, Tecktronics, Beaverton, OR, USA). The Hilbert transform and envelope detection algorithms were applied in order to further smooth the waveform in the time and frequency domains.

Figure 12 shows the echo waveforms and their spectrum data received from the bigeye tuna eye with red, green, and blue LED lights when the 25 MHz transducer was used. The acquired echo amplitudes of the transducer using red, green, and blue LEDs are 282 mV, and 1557 mV, and 2356 mV, respectively. The first echo signal response times of the red, green, and blue LEDs are 40.55 µs, 40.89 µs, and 40.95 µs, respectively. The center frequencies of the red, green and blue LEDs, with the −6 dB bandwidths in parentheses, are 20.24 MHz (30.47%), 22.68 MHz (39.85%), and 22.25 MHz (49.34%), respectively. These experimental results demonstrate the detection capability of the developed LEDA system, which can achieve relatively high echo sensitivity in the bigeye tuna eye.

A typical system employing laser technology is still an expensive and less-portable method that requires accurate laser control to avoid damages to eye tissues. To the best of our knowledge, there has never been an LEDA utilizing a Ramsden eyepiece for the study of ocular tissue properties in bovine and bigeye tuna eyes. Our developed system which comprises a pulsed LED and a custom designed Ramsden eyepiece is a cost-effective, safe, and compact method that still provides the capability to detect echo signals in the eye areas. Low frequency ultrasound transducers are typically used to obtain information deeper in the tissue while high frequency ultrasound transducers are usually used to obtain information from the eye surface. In that sense, our developed LEDA system was verified with both low and high frequency (>15 MHz) ultrasound transducers. Experimental results successfully demonstrated that the developed system using visible light wavelengths (red, green, and blue wavelengths) could adequately detect echo signals from the surface areas of the bovine and bigeye tuna eyes when using low frequency (10 MHz) and high frequency (25 MHz) ultrasound transducers, respectively. This work could provide the groundwork and also represents a low-cost, harmless and compact system for future realization in ophthalmology applications.