1.

Introduction

Myopia or nearsightedness is an ophthalmologic disorder that causes blurred vision and is usually corrected by wearing glasses or contact lenses.¹ When staring at nearby objects for extended periods of time, the ophthalmic lenses are deformed through tension in the musculus ciliaris and may temporarily have trouble focusing on a distant object. This type of nearsightedness is called refractive myopia or pseudomyopia, and it can be cured naturally over time or by medication that relaxes the tension in the musculus ciliaris, thereby allowing the lens to revert to the normal thickness. Due to the outbreak of COVID-19, the statistics in 2020 reported an increasing number of refractive myopia cases that have been possibly caused by environmental factors, including extended time spent performing desk-work and limited exposure to outdoor light.²

Pathologic nearsightedness or axial myopia, on the other hand, is more aggressive in nature and caused by the abnormal extension of the ocular fundus. The stage of progression of this ocular disorder is diagnosed by measuring the axial length between the cornea surface and the retina as schematically defined in Fig. 1. Due to the elongation of the axial length, which normally falls in a range between 22 and 25 mm,¹ the focal point of the eye is anomalously shifted off of the retina, reducing the clarity of visual perception. Axial myopia can also be associated with more serious intercurrent pathologies, including scleral staphyloma, glaucoma, and myopic macular degeneration, sometimes leading to schisis and retinal tears.¹ These syndromes possibly result in blindness, and it is therefore crucial to diagnostically distinguish cases of axial myopia from refractive myopia at the earliest possible age. At present, no definitive therapy or medication has been found to cure axial myopia, except for a few positive reports with low-concentration dosing of atropine (0.01%) is effective for schoolchildren to suppress further elongation of the axial length.^3,4 For this reason, ophthalmologic assessment of the axial length is being included in a large-scale vision-check on 9000 schoolchildren, organized by the Japan Ministry of Education, Culture, Sports, Science, and Technology (MEXT) for the next three years starting in 2021.

Fig. 1

Schematic illustration of ocular structure exhibiting axial myopia. Abnormal elongation of the axial length causes pathological shortsightedness.

Time-of-flight measurement of ultrasonic waves is usually used to determine the axial length of the eye, calculating the distances to the tissue boundaries that reflect the ultrasonic waves.⁵ For measurement, an ultrasonic probe sensor is brought into direct contact with the cornea surface or indirectly coupled with it using an eyecup filled with water. In either case, extreme caution must be used when handling the equipment to avoid injuring the delicate tissue, as well as to prevent ocular infections.

From a hygienic point of view, optical measurement of the axial length is preferable when performing pre-symptomatic checkups on large populations. Currently, the refractive power of the eye can be measured using, for instance, an auto refractometer/keratometer,⁶ and advanced versions of such instruments are equipped with a function to monitor the radius of curvature of the ocular fundus for further inspection. Fundoscopy based on optical coherence tomography (OCT) is a more powerful method to visualize the detailed tissue cross-section.^7,8 OCT is an imaging technology that acquires tomographic visual information similar to that provided by ultrasonic or x-ray computer tomography (x-ray CT) with imaging resolutions up to a few microns, which is finer than that of ultrasonic imaging by an order of magnitude. Compared with x-ray CT, OCT is more suitable for clinical and biological applications because it relies on infrared light and is therefore free from harmful radiation exposure.

In this paper, we review the fundamental principle of OCT and discuss a methodology to extend the measurement depth using a highly coherent light source. As an alternative method to the classic time-domain OCT (TD-OCT) measurement, in which the length of the reference arm in the optical interferometer is mechanically modulated, we use a wavelength tunable laser diode (LD) to perform Fourier-domain OCT or so-called swept-source OCT (SS-OCT). As a key component for such SS-OCT systems, we have developed a wavelength tunable LD using a microelectromechanical system (MEMS)-based electrostatic mirror that is coupled with a vertical-cavity surface-emitting laser (VCSEL) chip, which was originally invented by Iga and documented in detail in his recent review paper published elsewhere,⁹ forming a Fabry–Perot interferometer. Owing to the single-mode resonance, the coherence length and coherence revival length are extended, thereby enabling OCT observation through an object as large as the entire ocular globe with single-shot imaging. This paper includes extended results such as the large coherence length over 150 m, based on the precedent technical report presented at IEEE OMN 2019.¹⁰

2.

OCT Principle

The fundamental measurement method leading to OCT was developed in 1987 by Takada et al.,⁷ who demonstrated detection of failure in an optical waveguide that was formed into an interferometer illuminated by a low-coherence super luminescent diode (SLD); the methodology was called optical coherence-domain reflectometry, which was later used for ophthalmologic ocular diameter measurement at a high resolution of $10\mu \mathrm{m}$. In 1991, Huang et al.⁸ with MIT published a paper on OCT, which lead to the rapid development of OCT-related technologies, including ophthalmic measurement instruments on a commercial level in the 1990s. OCT today is widely accepted not only in the field of ophthalmology but also in cardiology,¹¹ dentistry,¹² and dermatology.¹³ Non-contact OCT is also preferred for industrial applications, such as laser welding monitoring¹⁴ and light-detection-and-ranging (LiDAR).¹⁵

Figure 2 illustrates a simplified analytical model for OCT measurement based on the Michelson–Morley interferometer. The probe light emitted from a light source is split into two branches: the reference arm and the sample arm. The light traveling in the reference arm is bounced back by the reflector and guided into the photodetector (PD) after traveling a round-trip distance of $2(z+\mathrm{\Delta }{z}_{\mathrm{r}})$, where $\mathrm{\Delta }{z}_{\mathrm{r}}$ is the adjustable position of the reflector. The electrical field of the light at the PD is written as^16,17

Fig. 2

Principle of OCT based on the Michelson–Morley interferometer.

When these two lights interfere, the total optical power received by the PD is calculated by the product of complex conjugates as

The first two terms are the dc components that can be eliminated using a balanced PD, and the third term depends on the difference between the two optical path lengths $2(\mathrm{\Delta }{z}_{\mathrm{s}}-\mathrm{\Delta }{z}_{\mathrm{r}})$ as well as the wavenumber of the probe light $k=2\pi /\lambda$, where $\lambda$ is the wavelength.

OCTs in the early stage used low coherence light sources with relatively broad bandwidths, such as SLDs⁷ and multi-mode lasers. Owing to the multiple modes contained within a bandwidth as schematically shown in Fig. 3(a), the waveform of light traveling in the space is described by the repetition of wave packets as shown in Fig. 3(b). Such a wave maintains its spatial coherence within the limited range along the traveling axis called the coherence length. Presuming a Gaussian distribution of laser power with a bandwidth of $\mathrm{\Delta }{\lambda }_{\mathrm{BW}}$, the coherence length is written as¹⁶

Fig. 3

Coherence length affected by the mode of the light source. (a) Spectral density of a multi-mode light source with Gaussian distribution and (b) its electrical field waveform along the axis of travel. Coherence is maintained only within the periodic coherence length. (c) Spectral density of a single-mode light source and (b) its electrical field waveform.

In practical implementations of TD-OCT systems, the position of the reference reflector $\mathrm{\Delta }{z}_{\mathrm{r}}$ is mechanically modulated to seek the peak OCT signal, and the resolution of the resulting spatial measurement is limited by the coherence length or the positioning precision of the reference reflector. Given a bandwidth $\mathrm{\Delta }{\lambda }_{\mathrm{BW}}$ is 50 nm around a center wavelength $\lambda$ of 1050 nm, the coherence length $l_{\mathrm{c}}$ is expected to be $9.7\mu \mathrm{m}$, which is comparable with the typical dimension of a biological cell. In OCT technology, the longitudinal scan to search for the depth of the reflection point is called the A-scan, whereas the lateral beam position control over the sample surface is called the B-scan as shown in Fig. 2. The orthogonal set of A- and B-scans, therefore, produces cross-sectional or volumetric images.

Due to the modulation mechanism of the reflector in the reference arm, the frame rate of TD-OCT is usually no faster than 30 fps.¹⁸ Aside from the penetration depth of light in the sample, the scan depth is usually limited by the mechanical stroke of the reflector, typically a few millimeters or less. Another limiting factor for the depth of an OCT scan is more inherent to the nature of the coherence of light. Given a representative cavity length $L$ in the laser unit, the round-trip distance within the cavity, $2L$, should be a multiple of the lasing wavelength $\lambda$ to maintain the oscillation, and therefore the phase shift after a round trip is written as

Superposition of multiple modes ($\nu$, $\nu +\mathrm{\Delta }\nu$, $\nu +2\mathrm{\Delta }\nu ,\cdots$) produces a beat in the oscillation envelope at a base tone frequency of $\mathrm{\Delta }\nu$; this envelope fluctuation manifests as the wave packets that repeatedly appear at a constant interval of $\mathrm{\Delta }{\nu }^{-1}$ in the time domain or at a constant spatial pitch called the coherence revival length $l_{\mathrm{cr}}=c/\mathrm{\Delta }\nu =2L$ in the space domain as shown in Fig. 3(b). As a result, the OCT signal intensifies not only at the phase matching condition of $\mathrm{\Delta }{z}_{\mathrm{s}}=\mathrm{\Delta }{z}_{\mathrm{r}}$ but also at multiple positions that fulfill $\mathrm{\Delta }{z}_{\mathrm{s}}=\mathrm{\Delta }{z}_{\mathrm{r}}+mL$, which causes ghost-like artifact images at false depths. The effect of coherent revival is more pronounced when the tunable cavity length $L$ is as large as a few millimeters to a centimeter, for instance, in the case of an external cavity laser.^19,20 Hence, TD-OCT optics with low coherence LDs have high axial resolution owing to the short coherence length but imaging depth is limited to a few millimeters.

When a VCSEL structure is adopted for a light source, on the other hand, the tunable cavity length $L$ can be made small in the order of a micron,²¹ and from Eq. (8), the mode separation $\mathrm{\Delta }\nu$ accordingly becomes large. Such a condition allows only one mode to be solely excited as shown in Fig. 3(c), excluding all the other modes outside the gain bandwidth of the laser medium. The output of such a single-mode laser becomes a continuous sinusoidal wave of a virtually infinite coherence length that is

Owing to the extended coherence length, the light signals from the reference and the sample arms would constructively interfere at countless positions of $\mathrm{\Delta }{z}_{\mathrm{r}}$ so long as $2k(\mathrm{\Delta }{z}_{\mathrm{s}}-\mathrm{\Delta }{z}_{\mathrm{r}})$ is a multiple of $2\pi$, thus the TD-OCT type analysis is incapable of identifying the exact point of reflection, $\mathrm{\Delta }{z}_{\mathrm{s}}$, by scanning the reference arm length $\mathrm{\Delta }{z}_{\mathrm{r}}$.

As an alternative method, the wavelength $\lambda$ and thus the wavenumber $k(=2\pi /\lambda )$ of the probe light itself can be scanned using a wavelength-tunable single-mode LD. When the wavelength is monotonically scanned from $\lambda$ to $\lambda +\mathrm{\Delta }\lambda$ as shown in Fig. 4(a), the corresponding change of the wavenumber is

Fig. 4

Principle of swept-source OCT using a single-mode laser. (a) Wavelength tuning for A-scan and (b) oscillation signal of OCT interference when sweeping the source wavelength, which is fast Fourier transformed in (c) to find the location of the reflection point.

The axial imaging resolution is equivalent to the counting accuracy of $N$ in Eq. (11). Provided that the difference between $N$ and $N+1$ is resolvable by measurement, the resolution is on the order of ${\lambda }^2/(2\mathrm{\Delta }\lambda )$. When the single-mode spectrum is modeled by the Gaussian profile, the longitudinal resolution is written in a more precise form as¹⁶

3.

Wavelength-Tunable VCSEL Structures

Wavelength-tunable VCSELs are categorized in two types, optically pumped^24–26 and electrically pumped (current injection),^27–29 depending on how the excitation power is introduced into the active layer. Optical pumped LDs usually have a large laser gain that leads to a relatively wide wavelength tuning range and large output power. Nevertheless, cost and reliability are significant drawbacks due to the complexity of device structures that require extra optical components. In this work, we adopted an electrically pumped half-VCSEL for the simplicity of the optics involved.

Figure 5(a) schematically illustrates the assembled structure of the MEMS tunable VCSEL developed in this work. A half-cavity VCSEL chip with a gain medium of strained InGaAs multi-quantum on a standard (100) GaAs substrate is developed in-house, in a layered structure similar to the one reported elsewhere;³⁰ no distributed Bragg reflector (DBR) is used as an upper reflector in the VCSEL chip but it is face-side-down coupled to an electrostatically controlled MEMS diaphragm mirror made of a silicon-on-insulator (SOI) wafer to form a tunable Fabry–Perot interferometer. As a half-cavity VCSEL, the upper surface of the MEMS mirror (facing inward the laser cavity) is high reflective-coated with ${\mathrm{SiO}}_2/{\mathrm{Ta}}_2{\mathrm{O}}_5$ multilayer, whereas the bottom surface is antireflective-coated with ${\mathrm{SiO}}_2/{\mathrm{Ta}}_2{\mathrm{O}}_5$ multilayer for an optical outlet. The two chips are assembled by thermo-compression bonding of the gold contact pads. The parallelism of the cavity is controlled by in-situ optical calibration of the height of the bonding pads using a dedicated measurement instrument during the bonding process. Figure 5(b) shows a finished chip photographed from the top. The chip will be later mounted on a metallic case with a hole so that the emitted light can be coupled to an optical fiber welded behind the case.

Fig. 5

Structure of the wavelength tunable LD. (a) Schematic illustration of chip assembly, an InGaAs chip on a silicon MEMS chip. (b) A VCSEL chip mounted on an electrostatic MEMS Fabry–Perot mirror.

The MEMS mirror is a disk diaphragm suspended with silicon hinges as schematically illustrated in Fig. 6(a), all made in the single crystalline layer of SOI. The voltage for electrostatic operation is applied to the suspended SOI structure with respect to the handle substrate so that the cavity length in the InGaAs layer is increased due to the electrostatic pull-down of the mirror’s height. Detail dimensions of the mirror and the suspensions are summarized in Table 1. The device parameters are chosen so that the fundamental mechanical resonant frequency is set around 80 kHz, and the operation voltage does not exceed 200 $V_{\mathrm{dc}}$ to achieve electrostatic pull-in. The actual operation voltage is lower than this upper limit, as the mirror’s stroke length is augmented through mechanical resonance. Figure 6(b) shows a photograph of the MEMS mirror chip seen from the SOI side before die-bonding.

Fig. 6

MEMS mirror structure for electrostatic operation. The mirror disk is suspended above the chip with an air gap made after selective sacrificial etching of the buried oxide. (a) Schematic structure as an analytical model and (b) a photograph of a bare chip before die-bonding.

Table 1

Design parameters for MEMS Fabry–Perot interferometer mirror.

4.

Optical Performance

Figure 7(a) shows the apparatus for optical performance measurement. The output of the tunable VCSEL is coupled to a multi-mode optical fiber and characterized using the optical spectrum analyzer and power meter. Figure 7(b) shows an example of a wavelength-tunable LD module assembled with a MEMS-controlled VCSEL chip. Semiconductor components such as VCSEL, SOA, and optical components were hermetically assembled in a sealed package, and controlled by an electrical circuit interface that provides both the injection current for the tunable VCSEL module and the electrostatic control voltage for the MEMS. The LD unit also gives a start trigger (A-trigger) for the depth scan (A-scan) that could be used to initiate the spatial beam steering (B-scan), for which MEMS optical scanners are frequently used.^31–34 It also generates another sampling trigger (K-trigger) at an equal wavelength interval.

Fig. 7

Optical apparatus for characterization. (a) Block diagram for optical performance measurement and (b) VCSEL swept-source module with a MEMS tunable VCSEL and SOA.

Figure 8 shows the optical output power as a function of injection current, measured at the peak power wavelength (1065 nm). The threshold current was 0.44 mA, and maximum deliverable power was 1.5 mW at an injection current of 8 mA. OCT measurement usually requires a probe power of more than 10 mW, and we therefore used a semiconductor optical amplifier (SOA) in the subsequent stage to enhance the output power of the LD module to 30 mW.

Fig. 8

Output power of LD as a function of injection current.

Figure 9 shows the lasing spectrum of the developed tunable LD, measured using an optical spectrum analyzer (AQ6370D, Yokogawa Test & Measurement Corporation) near the peak power wavelength. A single-mode resonance was realized by appropriately designing the resonator’s FSR to be wider than the effective band of the DBR. The side-mode suppression ratio (SMSR) was tuned to be greater than 40 dB by optimizing the aperture dimensions of the VCSEL and the MEMS mirror disk. This SMSR is sufficient to make the LD acceptable as a single-mode light source.

Fig. 9

Intensity spectrum of LD. SMSR of at least 40 dB is confirmed.

Output power profiles of the VCSEL (injection current 6 mA) were determined as shown in Fig. 10(a), at different dc voltages applied to control the cavity length of the electrostatic MEMS mirror. Individual longitudinal modes of above 25 dB were obtained over the whole tuning range between 1010 and 1090 nm when the MEMS mirror was operated with dc voltages of 100 to 190 V, as shown in Fig. 10(b). Continuous wavelength control over 89 nm with respect to the center wavelength 1050 nm was confirmed at room temperature without causing mode hopping. No laser output was observed for dc voltages of lower than 100 V because the wavelengths corresponding to the cavity lengths were outside the gain bandwidth of the laser medium. When the MEMS mirror was electrostatically operated at 100 kHz, the operation voltage could be lowered to 124 $V_{\mathrm{ac}}$ to achieve a continuous wavelength sweep in the same range as shown in Fig. 11; the spectrum was obtained by keeping the gate of spectrum analyzer open for 10 s to accommodate more than ${10}^6$ cycles of the wavelength scan. In addition, oscillation of the mirror at the resonant frequency (80 kHz) was found to be susceptibly influenced by the environment change. Therefore, we used a frequency slightly higher than the resonance (100 kHz) to set a margin in the oscillation amplitude so that the control electronics could maintain the oscillation level by adjusting the drive voltage.

Fig. 10

Wavelength tuning performance measured at different dc voltages applied to control the cavity length of the electrostatic MEMS mirror. (a) Spectrum range of tuning more than 89 nm. (b) Center wavelength as a function of operation voltage of the MEMS Fabry–Perot mirror.

Fig. 11

Continuous wavelength tuning with a MEMS mirror operated by a sinusoidal wave voltage at 100 kHz.

Figure 12 shows the temporal changes in the optical output power and the lasing wavelength scanned at 50 kHz. Unlike piezoelectrically driven actuator whose displacement is proportional to the applied voltage, the electromechanical behavior of the mirror in this work is described using an electrostatic parallel plate model whose displacement changes as a quadratic function of applied voltage when actuated at a frequency well below the mechanical resonance. As a result, the lasing wavelength also follows a quadratic function of the voltage, which is not convenient when performing FFT analysis that presumes a uniform frequency step size. Therefore, we used the K-trigger from the LD module to rearrange the acquired data into data strings of a uniform wavelength step. This data processing allowed the SS-OCT to function in a wide range of operation frequencies between 4 and 200 kHz. The swept-source operation can be performed at a frequency higher than the mechanical resonance (80 kHz) of the MEMS because wavelength tuning takes place during both strokes. Typical optical output power above 30 mW was obtained with the use of an SOA and when modulated at a duty ratio of 50%, more than 15 mW of optical power could be delivered to the OCT system, which meets the signal power requirements of most OCT applications for medical diagnosis.

Fig. 12

Wavelength sweep performance (power and wavelength) when operated at 50 kHz.

Owing to the single-mode resonance, the developed tunable VCSEL was expected to have a long coherence length of more than 100 m. We used a fiber-coupler Michelson–Morley interferometer, as schematically shown in Fig. 13(a), to determine the roll-off of the fringe interference intensity as a function of the path difference $\mathrm{\Delta }z$, as shown in Fig. 13(b); the travel distance has been converted to that in air taking the refractive index of the optical fiber into account, and the fringe intensity has been normalized by the value taken for $\mathrm{\Delta }z=0$. The coherence length, defined as the length beyond which the interference intensity attenuates by more than $-3\mathrm{dB}$, is thus shown to be longer than 150 m because the experimentally determined loss was no greater than $-0.5\mathrm{dB}$ at this length of optical path difference. The result suggested that the developed light source could also be used for long range LiDAR application.¹⁵

Fig. 13

Coherence length measurement of the developed light source. (a) Block diagraph of measurement apparatus and (b) measurement result showing a coherence length of more than 150 m.

5.

SS-OCT Performance

Figure 14 shows the block diagram of the SS-OCT system using a wavelength tunable VCSEL. The probe light from the light source is spatially scanned over the sample with a Galvano scanner, and its interference signal is received by a balanced photodetector (BPD). Analog-to-digital conversion is performed at 500 MHz using a data acquisition module (Flexible SS-OCT DAQ Board HAD-5200B-S, Santec Corporation) and an FFT on a personal computer (PC) to calculate the depth of the light-reflective feature in the sample. The PC also controls the Galvano scanner by the analog voltages applied through an amplifier (Amp).

Fig. 14

Optoelectrical block diagram for SS-OCT.

Owing to the wide tunable wavelength range and the fast modulation speed, SS-OCT was performed through different ranges of measurement depth using a single light source. Figure 15(a) shows an OCT image of a human eye, when the wavelength tuning range was set to be 40 nm. The scan speed of the wavelength was 20 kHz, and the data were acquired at 50% duty ratio, when the wavelength was swept upward only. Due to the fast frame rate of 40 fps, a clear OCT image was obtained without being affected by motion due to fibrillation in the eye muscles. The single-mode nature of the VCSEL also allowed a relatively large FSR, and thus a long coherence revival length, which allows us to image the entire eye in a single shot, including the anterior chamber and the retina. The axial length of the eye was instantly measured to be 25 mm, which was in the normal range for adults.

Fig. 15

OCT image of human ocular globe. (a) Entire view obtained by a single shot OCT, (b) close up image of the anterior chamber and the lens, and (c) close up image of the retina.

In addition to SS-OCT measurements over a short working distance such as ophthalmologic observation, the same optical system could also be used over longer distances when the wavelength tuning range was deliberately reduced by reprogrammable software. Figure 16(a) shows an object made of opaque plastic bricks placed at a 50-cm distance from the OCT aperture. By measuring the surface reflection, a 3D profile image of the object was reconstructed as shown in Fig. 16(b). Due to the long coherence length of over 150 m, OCT measurement of a relatively large object was thus possible without suffering from the coherence revival problem; this result implies that the SS-OCT system developed in this work could be used for alternative applications such as surface profilometry or laser range finding.

Fig. 16

Three-dimensional profile measurement by OCT over a long distance. (a) Target object placed at a 50-cm distance from the OCT system and (b) its color map profile.

Figure 17 compares the quality of SS-OCT images obtained using a conventional multi-mode LD and a single-mode VCSEL. A reel of semi-transparent adhesive tape placed in front of the OCT aperture was observed at four different distances. At the initial position, $\mathrm{\Delta }z=0$, images of both the multi-mode LD and the single-mode VCSEL clearly presented the layered structure of adhesive tape as shown in Figs. 17(a1) and 17(b1), respectively. When the reel was retracted by 3 mm, the images were equally displaced downward as shown in Figs. 17(a2) and 17(b2) until they slid off the field of view as shown in Figs. 17(a3) and 17(b3). When the object is retracted further, the OCT image should remain as blank as Fig. 17(b4) obtained by the single-mode VCSEL. However, the image obtained by the multi-mode LD presented a ghost image as shown in Fig. 17(a4). This artifact was caused by the repetition of wave packets shown in Fig. 3(b), which produced the false intensity-modulated signal affecting the FFT computation to determine the depth of reflection.

Fig. 17

Comparison of OCT images obtained with (a1)–(a4) a multi-mode LD and (b1)–(b4) a single-mode LD.

6.

Conclusions

Wavelength tunable VCSELs are one of the most appropriate applications of optical microsystems based on MEMS technology. A short-cavity LD can be assembled by putting a VCSEL chip onto an electrostatically tunable MEMS Fabry–Perot interferometer to realize a single-mode wavelength-tunable LD of a long coherence length as well as a long coherence revival length. In this work, an electrostatically actuated MEMS diaphragm mirror of $780\mu \mathrm{m}$ in diameter was developed by silicon micromachining using an SOI substrate and coupled with an InGaAs VCSEL chip to produce a wavelength-tunable VCSEL with a wide tuning range of 89 nm around a center wavelength of 1050 nm. Typical output power of 1.5 mW was obtained from an injection current of 8 mA. As a result of the short cavity length, the coherence length was longer than 150 m, which made the device suitable as a light source for an SS-OCT system that could be used to measure the ophthalmic axial length at high speed under 25 ms. In addition to ocular characterization, the same system was also found to be capable of performing long-range measurements, such as surface profilometry, LiDAR, and laser welding monitoring.