# Investigation of Light Parameters on Image Quality and Optical Coherence Tomography

Authors: Boka Fikadu; Bulcha Bekele; Leta Tesfaye Jule; Anatol Degefa; N. Nagaprasad; Krishnaraj Ramaswamy
Journal: International Journal of Optics
 (2021)

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## Abstract

In this work, image quality and optical coherence tomography were studied. The results of the study show that there is a very significant difference between ultrasound and optical coherence tomography to produce an image with a different wave. To understand this, we studied the basic principle of optical coherence tomography in the Michelson interferometer using monochromatic and broadband sources. Time-domain and spectral-domain measurements, which exist at the detector level, are briefly described using a glass sample. The time-domain signal strength of the Michelson interferometer using a broadband source is a Gaussian envelope.


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## Body

## 1. Introduction

Huang invented optical coherence tomography (OCT) in 1991, and it has since found various applications outside of ophthalmology. For example, OCT is also used to picture certain nontransparent tissues [1]. OCT (optical coherence tomography) system is an optical instrument that provides a cross-sectional image of the biological tissue with an axial resolution of less than 10 microns utilizing light waves [2]. Furthermore, optical coherence tomography (OCT) is a technique that is currently in use in medicine and biology and is capable of creating high-resolution and cross-sectional images of biological tissues [3]. Included in this category are both transparent tissues, including the eyes, and heavily scattering tissues, such as the skin [4]. OCT has very similar applications to ultrasound imaging, but instead of using time-of-flight measurements, OCT utilizes the interference nature of light waves to produce coherence gating [5]. One of the most important components of OCT is that there is no ionizing radiation, and it is not necessary to prepare a sample [6]. Additionally, OCT is comparatively safe when compared with another technique that uses X-rays because it uses light sources without ionizing radiation being involved. Furthermore, with the advantage of being a noninvasive (in vivo) technique, OCT systems show great potential in the future of medical diagnostics. Today, scanning of retinas to reveal defects in the underlying tissue is the area of most success for OCT, and standalone units are being sold commercially [4–6]. The OCT technique is limited to an imaging size of up to 1 mm below the surface of biological tissues [7]. OCT is specifically good at scanning the retina [8]. Because the retina is readily available to external light, optical coherence tomography (OCT) is particularly useful for diagnosing abnormalities [9]. The light enters the eyes, and the retina converts it into electric signals and passes them to the brain for the formation or reconstruction images [1, 2]. The major component of the retina is the optics disk, macula, and blood vessels. Using OCT, it is easy to see ten different tissue layers inside the retina [2, 5, 8]. Only about a decade ago, the first reports of OCT use in medicine were published in peer-reviewed journals [1, 5, 7]. Although its roots can be traced back to early research on white light interferometry, the discovery of optical coherence domain reflectometry (OCDR), a one-dimensional optical detection technique, is credited with giving rise to the technology [10]. It was initially designed for the purpose of detecting flaws in defective optical fibres and optical network components; nevertheless, its capacity to probe the eye as well as other biological tissues was quickly realized [11]. OCT is a modern variant of a Michelson interferometer, which worked by removing one side of the reference mirror and replacing it with a sample glass to determine the image of the tissue using monochromatic sources and broadband sources [12]. OCT is a type of optical coherence tomography that operates in both the time domain and the spectral domain [13]. For evaluating depth study in time-domain optical coherence tomography, the reference mirror must be moved; however, spectral-domain optical coherence tomography is a Fourier transform analysis performed without adjusting the mirror [2]. In this article, we explain the application of modern optical instruments, specifically for measurements using a Michelson interferometer. Additionally, we simulate the signal Fourier transforms of the materials and compare them with the results of an image of the sample. The primary goal of this study is to figure out the images of OCT using low coherence interference. As a result, time-domain and spectral-domain optical coherence tomography can be determined in broadband sources.


## 2. Principle of Optical Coherence Tomography

OCT has special characteristics, like it is noninvasive and is nondestructive. OCT is used to identify very small structures, and it is used to look under the skin. It can also be used to give information by producing a 3-dimensional image [14].


### 2.1. Interferences

Young’s double-slit experiment is the famous demonstration of optical interference and describes that the light from a single source radiating through two slits (or hole) can interfere with projection of an alternating fringe pattern of bright and dark bands on a screen [1, 6, 9]. These bright and dark fringes occur because of the constructive and destructive interferences of light, respectively. Depending on this bright and dark pattern, the light waves from the two slits are in phase and we add them together up to the resultant maximum amplitude called constructive interference, or when the light waves from the two slits are out of phase, we subtract up to the resultant minimum amplitude called destructive interference. That these two (constructive and destructive interferences) exist are based on the optical path length difference (OPD) between the slits and the same location on the screen [11, 13, 15].


### 2.2. Michelson Interferometer

The principle of optical coherence tomography originates with the Michelson interferometer, which was invented by A. A. Michelson in 1881. OCT is analogous to ultrasound, as they measure the back reflection intensity of infrared light beams instead of using the echoes of sound. Because of the rapid speed at which light propagates, it is impossible to quantify the back reflection intensity of OCT using electrical instruments [16]. Figure 1 shows a Michelson interferometer, which consists of two reflective mirrors, mirror 1 and mirror 2. Light is emitted from the light source, which hits the beam splitter, with half of the light going along path L1 and reflected back to the beam splitter while the other half goes along optical path L2 and is reﬂected back to the beam splitter [17]. These two light waves will interact with each other and be detected with the photodetector. Depending on the length diﬀerence between optical paths L1 and L2, either constructive or destructive interference will occur. Since both return beams will go through the beam splitter (a half-silvered mirror) again, they lose 50% of their intensity. In some more complicated setups, a polarizing beam splitter (half-silvered mirror) and wave retarders can be used to avoid this power loss.Figure 1
Schematic of the Michelson interferometer.OCT is a modern instrument that is used to produce an image, and image technology projects a light beam (820 nm) near the infrared wavelength. Figure2 shows the setup of OCT, similar to the Michelson interferometer setup. In this setup, only one reference mirror (a movable mirror) is used, and another, the standard mirror, has been changed with a sample of glass. The spectrum from the source of light is separated into different beams using the beam splitter. The probe beam enters the object, and the reference beam approaches the standard mirror at a predetermined distance from the reference mirror. Light reflected from different layers of the specimen is measured and compared to the light reflected from the reference mirror, which measures the echo duration or delay of the light reflected from the reference mirror. When light reflected from both the sample and reference mirrors arrives at the same time, a positive interference is formed. The interferometer integrates numerous data points over a depth of 2 mm to generate a tomogram of retinal architecture using the information from the data points [18].Figure 2
Schematic of OCT in Michelson interferometer.From Figure2, we have an incidence electric ﬁeld, coefficient of reflection, and transmission of a glass sample. Let us derive the equation of the incident electric ﬁeld of the sample and calculate the intensity at the detector. Consider the incident light as a plane wave, where the net ﬁeld at the photodetector includes the electric ﬁeld coming from L1 of the interferometer E0(t,τ) = Eeiω(t+τ) and the electric ﬁeld coming from L2 as E0(t) = Eeiωt.


## 2.1. Interferences

Young’s double-slit experiment is the famous demonstration of optical interference and describes that the light from a single source radiating through two slits (or hole) can interfere with projection of an alternating fringe pattern of bright and dark bands on a screen [1, 6, 9]. These bright and dark fringes occur because of the constructive and destructive interferences of light, respectively. Depending on this bright and dark pattern, the light waves from the two slits are in phase and we add them together up to the resultant maximum amplitude called constructive interference, or when the light waves from the two slits are out of phase, we subtract up to the resultant minimum amplitude called destructive interference. That these two (constructive and destructive interferences) exist are based on the optical path length difference (OPD) between the slits and the same location on the screen [11, 13, 15].


## 2.2. Michelson Interferometer

The principle of optical coherence tomography originates with the Michelson interferometer, which was invented by A. A. Michelson in 1881. OCT is analogous to ultrasound, as they measure the back reflection intensity of infrared light beams instead of using the echoes of sound. Because of the rapid speed at which light propagates, it is impossible to quantify the back reflection intensity of OCT using electrical instruments [16]. Figure 1 shows a Michelson interferometer, which consists of two reflective mirrors, mirror 1 and mirror 2. Light is emitted from the light source, which hits the beam splitter, with half of the light going along path L1 and reflected back to the beam splitter while the other half goes along optical path L2 and is reﬂected back to the beam splitter [17]. These two light waves will interact with each other and be detected with the photodetector. Depending on the length diﬀerence between optical paths L1 and L2, either constructive or destructive interference will occur. Since both return beams will go through the beam splitter (a half-silvered mirror) again, they lose 50% of their intensity. In some more complicated setups, a polarizing beam splitter (half-silvered mirror) and wave retarders can be used to avoid this power loss.Figure 1
Schematic of the Michelson interferometer.OCT is a modern instrument that is used to produce an image, and image technology projects a light beam (820 nm) near the infrared wavelength. Figure2 shows the setup of OCT, similar to the Michelson interferometer setup. In this setup, only one reference mirror (a movable mirror) is used, and another, the standard mirror, has been changed with a sample of glass. The spectrum from the source of light is separated into different beams using the beam splitter. The probe beam enters the object, and the reference beam approaches the standard mirror at a predetermined distance from the reference mirror. Light reflected from different layers of the specimen is measured and compared to the light reflected from the reference mirror, which measures the echo duration or delay of the light reflected from the reference mirror. When light reflected from both the sample and reference mirrors arrives at the same time, a positive interference is formed. The interferometer integrates numerous data points over a depth of 2 mm to generate a tomogram of retinal architecture using the information from the data points [18].Figure 2
Schematic of OCT in Michelson interferometer.From Figure2, we have an incidence electric ﬁeld, coefficient of reflection, and transmission of a glass sample. Let us derive the equation of the incident electric ﬁeld of the sample and calculate the intensity at the detector. Consider the incident light as a plane wave, where the net ﬁeld at the photodetector includes the electric ﬁeld coming from L1 of the interferometer E0(t,τ) = Eeiω(t+τ) and the electric ﬁeld coming from L2 as E0(t) = Eeiωt.


## 3. Results and Discussion

In the previous section, we have discussed the principles of OCT and the way OCT can be used like a Michelson interferometer. However, in this case, we review the analysis, discussion, and simulation of this project. The intensity of the Michelson interferometer was simulated, and the signal intensity of the Michelson interferometer in monochromatic and broadband sources was simulated. The signal intensity of OCT in a Michelson interferometer, when one reference mirror is replaced by a glass sample which has a refractive index of 1.5 and thickness of 1 mm, using monochromatic and broadband sources was simulated [19].


### 3.1. Simulations of Signal from the Michelson Interferometer

We simulated the intensity with the function of time at a detector. In this simulation, we used the central wavelength (λ0) as 1 μm and the spectral width (∆λ) as 100 nm for the light source and the velocity and position of the mirror as constant. The intensity which exists at the detector in the Michelson interferometer, with an incident wave as a function of time, is shown in Figure 3.Figure 3
Intensity of the Michelson interferometer.When the time was zero, the maximum intensity existed and the entire incident light did not occur. We simulated the signal intensity of a monochromatic source, as shown in Figure4. The signal intensity of the monochromatic source was simulated, where the horizontal axis shows the time difference between the movable mirror and the fixed mirror. In this simulation, we used the central wavelength (λ0) as 1 μm and the spectral width (∆λ) as 100 nm for the light source and the velocity and orientation of the mirror as constant. Its greatest possible amplitude refers to constructive interference as well as the minimum amplitude refers to destructive interference. When the time difference is zero, the reflectance is maximum and this is called constructive interference [20].Figure 4
Signal intensity of a monochromatic source.We simulated the signal intensity of the Michelson interferometer using a broadband coherent source, as shown in Figure5. This simulation of signal intensity has a Gaussian envelope [21]. In this case, we have some amount of continuous broadband sources, and we used the central wavelength (λ0) as 1 μm and the spectral width (∆λ) as 100 nm for the light source, where velocity and position of the mirror were constant. For this signal intensity, the movable mirror is of 1.5 ps. The horizontal axis shows the time difference of the movable mirror.Figure 5
Signal intensity of the broadband coherent source.From this Michelson interferometer, the signal intensity of light with a Gaussian spectrum as time is either increased or decreased; the output signal intensity started to oscillate. In this case, when we move the reference mirror by half-length, we get a different fringe pattern at each time.


### 3.2. Simulations of OCT in a Michelson Interferometer

We simulated signal intensity at the detector using a monochromatic source. In this case, one of the reference mirrors is replaced by a sample of glass. This sample glass has a thickness of 1 mm and a refractive index of 1.5. From the setup, we measure the reflection and transmission of the sample of glass as a function of time. First, we calculated the electric ﬁeld, where the Fresnel equations are of perpendicular incidence. That is, there would be a reﬂection at the ﬁrst surface and off the second surface and then also multiple reﬂections, which are called Fabry–Perot reflections [22]. The number of reflections we took into account would depend on the duration of the scan. The signal intensity of OCT in a Michelson interferometer using a monochromatic source with a long coherence length like a variable of time is shown in Figure 6. The maximum amplitude is for constructive interference, and the minimum amplitude is for destructive interference. When the time difference is zero, the reflectance is maximum and it is called constructive interference. This means the monochromatic signal intensity fringes are in phase only for zero time [23–28].Figure 6
Signal intensity of monochromatic sources.Figure7 shows the signal intensity of OCT in a Michelson interferometer using a broadband source. The central wavelength of (λ0) 1 μm and the spectral width (∆λ) of 100 nm for the light source were simulated. Signal intensity for the optical path length of the sample glass and the movable mirror was matched to the narrow coherence length as the light source used low coherence (broadband sources). The movable mirror started to scan when the optical path length of the reflections from within the sample glass matched each other. The incoming light source was split into two by the beam splitter. This means that when the incoming light passed through two different path lengths L1 and L2, then it was collinearly superimposed at the beam splitter, the two pulses reﬂected in each arm of the interferometer, and one of the arm’s lengths is increased, the distance causing a delay on recombining. The fundamental wavelength was rejected when the sample glass is detected by a photodetector as a function of the width of the time autocorrelation=2nd/c between the pulses. Since the refractive index and thickness of the glass are 1.5 and 1 mm, respectively, based on these values, we calculated the width of time = 10 picoseconds (10 ps) and frequency of 1 × 1012 Hertz (1 THz). The time delay at the detector using the width of the time pulse was calculated, where the central wavelength was (λ0) 1 μm and the spectral width (∆λ) was 100 nm, and the result was 3.3 ps.Figure 7
Signal intensity of a broadband coherent source.In this time-domain, OCT, three of these pulses have the same approximate width but diﬀerent heights. In the simplest method, we measured the shape of the pulse as changing with the distance of the time depth of the reference mirror and then we could see the signal intensity of our sample glass. The time delay of the movable mirror in this signal intensity of OCT was twice the time delay of the movable mirror in the signal intensity of Michelson interferometry. Since we have the values of the refractive index of glass, 1.5, and the thickness of the glass, 1 mm, we easily simulated the electric ﬁeld. Additionally, we have some constant values, such as the reﬂection coeﬃcient and transmission coeﬃcient, as well as the values of the angular frequency (ω) and tau (τ), also being constant. After we simulated the electric ﬁeld, we found the Fourier transform of this electric ﬁeld. This Fourier transform of the electric ﬁeld is the spectral domain of the OCT. We measured this spectral domain of the OCT without moving the mirror, and we only focused the Fourier transform of an electric ﬁeld of a sample glass [29–34].


## 3.1. Simulations of Signal from the Michelson Interferometer

We simulated the intensity with the function of time at a detector. In this simulation, we used the central wavelength (λ0) as 1 μm and the spectral width (∆λ) as 100 nm for the light source and the velocity and position of the mirror as constant. The intensity which exists at the detector in the Michelson interferometer, with an incident wave as a function of time, is shown in Figure 3.Figure 3
Intensity of the Michelson interferometer.When the time was zero, the maximum intensity existed and the entire incident light did not occur. We simulated the signal intensity of a monochromatic source, as shown in Figure4. The signal intensity of the monochromatic source was simulated, where the horizontal axis shows the time difference between the movable mirror and the fixed mirror. In this simulation, we used the central wavelength (λ0) as 1 μm and the spectral width (∆λ) as 100 nm for the light source and the velocity and orientation of the mirror as constant. Its greatest possible amplitude refers to constructive interference as well as the minimum amplitude refers to destructive interference. When the time difference is zero, the reflectance is maximum and this is called constructive interference [20].Figure 4
Signal intensity of a monochromatic source.We simulated the signal intensity of the Michelson interferometer using a broadband coherent source, as shown in Figure5. This simulation of signal intensity has a Gaussian envelope [21]. In this case, we have some amount of continuous broadband sources, and we used the central wavelength (λ0) as 1 μm and the spectral width (∆λ) as 100 nm for the light source, where velocity and position of the mirror were constant. For this signal intensity, the movable mirror is of 1.5 ps. The horizontal axis shows the time difference of the movable mirror.Figure 5
Signal intensity of the broadband coherent source.From this Michelson interferometer, the signal intensity of light with a Gaussian spectrum as time is either increased or decreased; the output signal intensity started to oscillate. In this case, when we move the reference mirror by half-length, we get a different fringe pattern at each time.


## 3.2. Simulations of OCT in a Michelson Interferometer

We simulated signal intensity at the detector using a monochromatic source. In this case, one of the reference mirrors is replaced by a sample of glass. This sample glass has a thickness of 1 mm and a refractive index of 1.5. From the setup, we measure the reflection and transmission of the sample of glass as a function of time. First, we calculated the electric ﬁeld, where the Fresnel equations are of perpendicular incidence. That is, there would be a reﬂection at the ﬁrst surface and off the second surface and then also multiple reﬂections, which are called Fabry–Perot reflections [22]. The number of reflections we took into account would depend on the duration of the scan. The signal intensity of OCT in a Michelson interferometer using a monochromatic source with a long coherence length like a variable of time is shown in Figure 6. The maximum amplitude is for constructive interference, and the minimum amplitude is for destructive interference. When the time difference is zero, the reflectance is maximum and it is called constructive interference. This means the monochromatic signal intensity fringes are in phase only for zero time [23–28].Figure 6
Signal intensity of monochromatic sources.Figure7 shows the signal intensity of OCT in a Michelson interferometer using a broadband source. The central wavelength of (λ0) 1 μm and the spectral width (∆λ) of 100 nm for the light source were simulated. Signal intensity for the optical path length of the sample glass and the movable mirror was matched to the narrow coherence length as the light source used low coherence (broadband sources). The movable mirror started to scan when the optical path length of the reflections from within the sample glass matched each other. The incoming light source was split into two by the beam splitter. This means that when the incoming light passed through two different path lengths L1 and L2, then it was collinearly superimposed at the beam splitter, the two pulses reﬂected in each arm of the interferometer, and one of the arm’s lengths is increased, the distance causing a delay on recombining. The fundamental wavelength was rejected when the sample glass is detected by a photodetector as a function of the width of the time autocorrelation=2nd/c between the pulses. Since the refractive index and thickness of the glass are 1.5 and 1 mm, respectively, based on these values, we calculated the width of time = 10 picoseconds (10 ps) and frequency of 1 × 1012 Hertz (1 THz). The time delay at the detector using the width of the time pulse was calculated, where the central wavelength was (λ0) 1 μm and the spectral width (∆λ) was 100 nm, and the result was 3.3 ps.Figure 7
Signal intensity of a broadband coherent source.In this time-domain, OCT, three of these pulses have the same approximate width but diﬀerent heights. In the simplest method, we measured the shape of the pulse as changing with the distance of the time depth of the reference mirror and then we could see the signal intensity of our sample glass. The time delay of the movable mirror in this signal intensity of OCT was twice the time delay of the movable mirror in the signal intensity of Michelson interferometry. Since we have the values of the refractive index of glass, 1.5, and the thickness of the glass, 1 mm, we easily simulated the electric ﬁeld. Additionally, we have some constant values, such as the reﬂection coeﬃcient and transmission coeﬃcient, as well as the values of the angular frequency (ω) and tau (τ), also being constant. After we simulated the electric ﬁeld, we found the Fourier transform of this electric ﬁeld. This Fourier transform of the electric ﬁeld is the spectral domain of the OCT. We measured this spectral domain of the OCT without moving the mirror, and we only focused the Fourier transform of an electric ﬁeld of a sample glass [29–34].


## 4. Conclusions

In our work, the application of nanotechnology in integrating OCT with the Michelson interferometer was realized. It is evident that the most important part of an OCT is the time domain and spectral domain. The time domain is based on a moving mirror, but the spectral domain is not based on this moving mirror; it is based on the Fourier transform of an electric ﬁeld. OCT has many applications in hospitals and industries, but it is mostly used on transparent materials or tissues. OCT is a modern technique that is used to create two- or three-dimensional images without involving any ionizing radiation. The way we measured the signal intensity at the detector in OCT is the same method as for the Michelson interferometer. However, we replaced the ﬁxed mirror with a sample of glass. We then talked about the time domain and spectral domain using a broadband source and a sample glass instead of a reference mirror on one side. We have shown from our results and simulation that the time domain generates ultrafast laser pulses in the range of picoseconds. Some of the characteristics of the pulses were computed, such as their ultrafast laser pulse duration (ps), repetition time, and intensity signal. As our results show, the numerical simulation of using the auto-correlation function to determine the temporal size of ultrafast pulse durations took 10 ps in the time domain of OCT integrated nanotechnology inference was concluded, indicating that the time domain is one of the best techniques for generating ultrafast laser pulses.



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*Source: 2322858-2021-11-26.xml*