Method for measuring nonlinear refractive index coefficient of cornea of living body through reflection-type spectrum

Abstract

The invention discloses a method for measuring a nonlinear refractive index coefficient of a cornea of a living body through a reflection-type spectrum, which comprises the following steps of: after a reflection spectrum obtained after interaction of femtosecond laser and the cornea is subjected to diffuse reflection through a scattering sheet, receiving an emergent spectrum signal on the surface of a medium by using an optical fiber head, and coupling with a spectrograph to obtain a spectrum shape; and obtaining the nonlinear refractive index coefficient of the cornea through a relation model between the spectral shape and the nonlinear refractive index coefficient. The method for measuring the nonlinear refractive index coefficient of the cornea through the reflection type spectrum method has the advantages that the device is simple, the signal-to-noise ratio is high, z-axis scanning is not needed, and the method has good application prospects in the aspects of measurement of the nonlinear refractive index coefficient of biological tissue such as measurement of the nonlinear refractive index coefficient of the cornea of a living body.

Description

Technical Field

[0001] The present invention belongs to the technical field of photoelectric detection, and more specifically, relates to a method for measuring the nonlinear refractive index coefficient of a living cornea using a reflective spectrum. Background Art

[0002] Precise and personalized femtosecond laser refractive surgery system is the future development trend. Femtosecond laser has the characteristics of short pulse width and high peak power. It will produce nonlinear optical effect in the process of interaction with tissue, thus leading to deviation of corneal stroma cutting amount: when the peak power of laser is greater than the corneal self-focusing threshold power (P c ), the focal position caused by the intensity-dependent refractive index n=n0+n2I (n0: linear refractive index of the material; n2: nonlinear refractive index coefficient of the material; I: light intensity of the laser) is different from the focal position predicted by linear Gaussian beam optics. If the cornea's n2 is large enough, it will cause a displacement of tens of microns, thereby causing corneal cutting surface errors, as well as the resulting refractive correction errors and additional high-order aberrations, which will affect the accuracy of the surgery and the patient's postoperative visual quality. In addition, the nonlinear refractive index coefficient of the cornea may vary from person to person. Therefore, it is very important to accurately measure the nonlinear refractive index coefficient of the living cornea, perform personalized pre-compensation for cutting depth and cutting surface shape, and improve the visual quality after correction.

[0003] In 1990, Sheik-Bahae et al. proposed the z-scan technique for characterizing the nonlinear refractive index coefficient of materials. This method has the advantages of simple optical path and accurate measurement. The z-scan technique has developed into the most classic and widely used method for measuring the nonlinear refractive index coefficient of media in the industry. The optical path diagram of this method is as follows Figure 1 As shown. The core idea is to convert the wavefront distortion caused by the nonlinear optical process into the intensity distribution of the far-field light spot that is easy to detect. However, when the random wavefront distortion caused by the surface roughness of the sample is much larger than the wavefront distortion caused by the nonlinear process, the light spot intensity in the far field will be affected by scattering, and the z-scanning technology will no longer be applicable. Therefore, the nonlinear refractive index coefficient of the scattering medium has become a difficult problem. In recent years, the spectral domain z-scanning method has been proposed. Its core idea is to replace the spatial domain with the spectral domain, that is, to measure the nonlinear effect of the medium based on the principle of spectral broadening caused by self-phase modulation in the nonlinear optical effect. This method can avoid the interference caused by scattering and has the advantages of high sensitivity and signal-to-noise ratio. At present, this method only has the transmission method, and the medium needs to be scanned on the z-axis. However, for the measurement of the nonlinear refractive index coefficient of some special media, such as the nonlinear refractive index coefficient of the living cornea, the transmission spectral domain z-scanning method is no longer applicable. For example, Miclea et al. used the z-scanning method to measure the nonlinear refractive index coefficient of the ex vivo pig cornea to be 2×10 -19 m 2 / W, overturning the conclusion that the nonlinear refractive index of the cornea is approximately equal to that of water. The scattering properties of the in vitro cornea have a great influence on the measurement results, and about 100 repeated measurements are required to obtain accurate results.

[0004] In 2010, Samineni et al. proposed a new z-scan technique for measuring the nonlinear refractive index of lipid solutions. The optical path diagram is shown in Figure 2 As shown. The technology first uses an acousto-optic modulator (AOM) to suppress the peak area of ​​the initial spectrum, thereby forming a "hole" spectrum. Then, after the light beam passes through the nonlinear medium, the "hole" of the spectrum will be "filled" by the self-phase modulation effect. Finally, the nonlinear refractive index coefficient of the medium is calculated based on the spectral deformation before and after the medium. This "hole" filling method avoids the interference caused by scattering in the principle of detection, and has high sensitivity and signal-to-noise ratio. The "hole" filling method reflects a ray of hope for the feasibility of measuring the nonlinear refractive index coefficient of biomaterials, but this method requires a spectrum shaping system and the optical path is relatively complex.

[0005] The patent publication number is: CN115266642A, and the name is a spectral domain z-scanning method for measuring the nonlinear refractive index coefficient of a strong scattering medium. It is the result of the previous research of this team. The patent proposes a transmission spectral domain z-scanning method. The optical path diagram is shown in Figure 3 As shown. By quantifying the size of the spectral broadening, a relationship model between the spectral broadening and the nonlinear refractive index coefficient n2 is established. This method can successfully measure the nonlinear refractive index coefficient of scattering media such as the in vitro cornea. This method simplifies the optical measurement device and has great prospects in the characterization of the nonlinear refractive index coefficient of rough media. However, this method is based on transmission measurement and requires scanning the z-axis of the medium. However, for the nonlinear refractive index measurement problems of some special media, such as the nonlinear refractive index measurement of the living cornea, the transmission spectral domain z-scanning method is no longer applicable. Summary of the invention

[0006] In order to overcome the shortcomings of existing methods for measuring the nonlinear refractive index of the cornea, such as low signal-to-noise ratio, complex equipment, and the need for z-axis scanning, the present invention proposes a reflective spectroscopy method to measure the nonlinear refractive index of the cornea, providing a solution to the problem of measuring the nonlinear refractive index of the living cornea.

[0007] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is:

[0008] A reflective spectral method for measuring the nonlinear refractive index coefficient of a living cornea includes a reflective spectrum after interaction between a femtosecond laser and the cornea, diffuse reflection by a scattering sheet, receiving an outgoing spectral signal on the surface of a medium with an optical fiber head and coupling with a spectrometer to obtain a spectral shape, and obtaining the nonlinear refractive index coefficient of the cornea through a relationship model between the spectral shape and the nonlinear refractive index coefficient.

[0009] Preferably, the wavelength of the femtosecond laser is 760-840 nm, the repetition pulse is 1 kHz, the pulse width is 50 fs, and the lens f=100 mm.

[0010] Preferably, the medium is confined by a fixture within a circle with a diameter of 8 mm, and the distance between the medium and the scattering plate is 2.4 cm.

[0011] Preferably, the gain parameter of the spectrometer is 100, and the exposure time is 1 s.

[0012] Preferably, the relationship model between the spectral shape and the nonlinear refractive index coefficient is that when the light pulse is transmitted along the z direction in the time domain t and the spatial domain r, the nonlinear transmission equation can be written as:

[0013]

[0014] The above equation includes spatial diffraction, pulse group velocity dispersion, self-focusing and plasma defocusing effects, and energy loss; where the initial light field distribution can be expressed as:

[0015]

[0016] The output pulse can be numerically solved by equation (1) using the finite difference method; the output pulse spectrum E(r, ω, z) is obtained by Fourier transform:

[0017]

[0018] So the power spectrum of the pulse is:

[0019] P=E(r,ω,z)·E * (r,ω,z) (4)

[0020] In order to quantify the spectral shape, it was previously proposed to use the transmittance T to quantify:

[0021]

[0022] Where F(λ) is the output spectrum and F′(λ) is the incident spectrum, and λ1 and λ2 are the selected integration windows.

[0023] Technical effects and advantages of the present invention:

[0024] The reflective spectroscopy method of the present invention measures the nonlinear refractive index coefficient of the cornea, has the advantages of simple device, high signal-to-noise ratio, and no need for z-axis scanning, and has good application prospects in the measurement of the nonlinear refractive index coefficient of biological tissues, such as the measurement of the nonlinear refractive index coefficient of the living cornea. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of the optical path diagram of the existing Z scanning technology.

[0026] Figure 2 Schematic diagram of the optical path of the existing "hole filling" method.

[0027] Figure 3 Schematic diagram of the optical path of the existing spectral domain z-scanning technology.

[0028] Figure 4 These are the emission spectra after the action of different incident energy lasers and different linear refractive index coefficients in Example 1; wherein (a) is the emission spectrum after the interaction between the laser and the medium under different incident energies; and (b) is the emission spectrum after the interaction between the laser and the medium with different nonlinear refractive index coefficients.

[0029] Figure 5 is the relationship between incident energy, spectral transmittance and n2 coefficient.

[0030] Figure 6 The figure is a schematic diagram of the optical path for measuring the nonlinear refractive index coefficient of a medium using the reflective spectroscopy method of the present invention.

[0031] Figure 7 is the emission spectrum under different incident energies DETAILED DESCRIPTION

[0032] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0033] In the description of the present invention, it should be noted that the terms "upper", "lower", "inner", "outer", "top / bottom" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description. They do not indicate or imply that the device or component referred to must have a specific position, be constructed and operated in a specific position, and therefore cannot be understood as limiting the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0034] Theoretical analysis:

[0035] The formation of femtosecond laser filaments is a complex nonlinear optical process, which is the result of the dynamic interaction of various optical effects. When the light pulse is transmitted along the z direction in the time domain t and the spatial domain r, the nonlinear transmission equation can be written as:

[0036]

[0037] The above equation includes spatial diffraction, pulse group velocity dispersion, self-focusing and plasma defocusing effects, and energy loss; where the initial light field distribution can be expressed as:

[0038]

[0039] The output pulse can be numerically solved by equation (1) using the finite difference method; the output pulse spectrum E(r, ω, z) is obtained by Fourier transform:

[0040]

[0041] So the power spectrum of the pulse is:

[0042] P=E(r,ω,z)·E * (r,ω,z) (4)

[0043] When a parallel femtosecond laser with a central wavelength of 800nm, a repetition rate of 1kHz, and a pulse width of 50fs is focused by a lens f=100mm into a 1.5mm medium, the output spectrum can be simulated according to equations (3) and (4). Changing the incident laser energy and the nonlinear refractive index of water will produce output spectra of different shapes. Figure 4 (a) shows that when the n2 coefficient of water is 2×10 -16 cm 2 / W, and the spectra of the output light field are obtained when the incident energy is 10nJ, 50nJ, and 100nJ respectively. Figure 4 (b) shows the simulation results of the emission spectrum when the laser incident energy is 50nJ and the water has different n2 coefficients.

[0044] From the theoretical analysis, it can be seen that the shape of the output spectrum is closely related to the incident energy and the nonlinear refractive index coefficient. As the energy and the nonlinear optical refractive index increase, the spectrum shows a trend of decreasing intensity in the center band and increasing intensity in the edge band. Therefore, we can obtain the nonlinear refractive index coefficient of the medium by measuring the spectral shape of the output laser. In order to quantify the spectral shape, we previously proposed to quantify it using the transmittance T:

[0045]

[0046] Where F(λ) is the output spectrum and F′(λ) is the incident spectrum. λ1 and λ2 are the selected integral windows. Based on the above laser parameters, we established a relationship model between the incident energy and the spectral transmittance and nonlinear refractive index coefficient, as shown in Figure 5 shown.

[0047] Example 1

[0048] Experimental verification:

[0049] A femtosecond laser chirped pulse amplifier model Legend-Elite-III-USP from Coherent was used to generate a pulsed laser with a central band of 800nm, a repetition pulse of 1kHz, and a spot waist radius of 2.5mm. The optical path diagram was constructed as shown in the figure below. Figure 6 As shown, the incident laser is first focused into the medium by a lens with f=100mm. The medium is confined by a fixture within a circle with a diameter of 8mm. The light beam can only pass through the circle. After interacting with the medium, the outgoing light is incident on the paper. The distance between the paper and the medium is 2.4cm. After diffuse reflection of the paper, the optical fiber head is used to receive the outgoing spectrum signal on the surface of the medium and couple it into the spectrometer (model: SR-750-A). Due to the diffuse reflection of the paper, the reflected spectrum signal is very weak, so the gain parameter of the spectrometer needs to be adjusted to 100, and the exposure time is 1s. In order to avoid the influence of diffuse reflection on the intensity of the spectral signal and thus affect the spectral shape, all the collected spectral signals are energy normalized.

[0050] Water is selected as the measurement medium. Many studies use water instead of cornea because the nonlinear refractive index coefficients of water and cornea are very close. Water is confined in the fixture, and the thickness of water is about 1.5mm. A neutral filter is used to adjust the incident power. When the incident power is about 70μW and 150μW, the measured output spectrum is as follows Figure 7 As shown in the red and blue spectral curves in the figure, it is obvious that the greater the power, the greater the deformation of the output spectrum, which is consistent with the conclusion obtained from theoretical analysis. In order to obtain an output spectrum without deformation, when the incident power is 70μW, the water medium is removed from the light path, and the output spectrum is obtained as follows Figure 7 The nonlinear refractive index of air is three orders of magnitude smaller than that of water, so at low power, air will hardly change the shape of the incident spectrum. We can use formula (5) to calculate Figure 7 The size of the deformation of the output spectrum, that is, the transmittance log 10 T v Indicates the magnitude of spectral deformation, and the T values ​​are 0.958 and 0.789 respectively, so log 10 T vare -1.38 and -0.675 respectively. It is worth noting that at a higher peak power, higher-order nonlinear optical effects may occur, so we generally use log 10 T v Keep it between -2 and -0.5. Finally, we Figure 5 Incident energy E and spectral deformation log 10 T v and the relationship between the nonlinear refractive index coefficient n2, the nonlinear refractive index coefficient of water is 1.6×10 -16 cm 2 / w and 1.5×10 -16 cm 2 / w, which is consistent with the nonlinear refractive index of water reported in the literature as 2×10 -16 cm 2 / w is very close, which shows that reflectance spectroscopy can measure the nonlinear refractive index of water. This technology has great prospects in measuring the nonlinear refractive index of living cornea.

[0051] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for measuring the nonlinear refractive index coefficient of the cornea of ​​a living body by using reflective spectroscopy, characterized in that: It includes the reflection spectrum after the interaction between the femtosecond laser and the cornea. After diffuse reflection from a scattering plate, an optical fiber head is used to receive the output spectrum signal on the surface of the medium and coupled to a spectrometer to obtain the spectrum shape. The nonlinear refractive index coefficient of the cornea is obtained through a relationship model between the spectrum shape and the nonlinear refractive index coefficient.

2. The method for measuring the nonlinear refractive index coefficient of the living cornea by reflective spectroscopy according to claim 1, characterized in that: The wavelength of the femtosecond laser is 760-840nm, the repetition pulse is 1kHz, the pulse width is 50fs, and the lens f=100mm.

3. The method for measuring the nonlinear refractive index coefficient of the living cornea by reflective spectroscopy according to claim 1, characterized in that: The medium is confined by a fixture in a circle with a diameter of 8 mm, and the distance between the medium and the scattering plate is 2.4 cm.

4. The method for measuring the nonlinear refractive index coefficient of the living cornea by reflective spectroscopy according to claim 1, characterized in that: The gain parameter of the spectrometer is 100, and the exposure time is 1 s.

5. The method for measuring the nonlinear refractive index coefficient of the living cornea by reflective spectroscopy according to claim 1, characterized in that: The relationship between the spectral shape and the nonlinear refractive index coefficient is modeled as follows: when the light pulse is transmitted along the z direction in the time domain t and the spatial domain r, the nonlinear transmission equation can be written as: The above equation includes spatial diffraction, pulse group velocity dispersion, self-focusing and plasma defocusing effects, and energy loss; where the initial light field distribution can be expressed as: The output pulse can be numerically solved by equation (1) using the finite difference method; the output pulse spectrum E(r, ω, z) is obtained by Fourier transform: So the power spectrum of the pulse is: P=E(r,ω,z)·E * (r,ω,z) (4)。 6. The method for measuring the nonlinear refractive index coefficient of the living cornea by using reflective spectroscopy according to claim 5, characterized in that: In order to quantify the spectral shape, it was previously proposed to use the transmittance T to quantify: Where F(λ) is the output spectrum, F′(λ) is the incident spectrum, and λ1 and λ2 are the selected integration windows.

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