CN112986185A - Optical material refractive index spectrum measurement system and method based on phase detection - Google Patents
Optical material refractive index spectrum measurement system and method based on phase detection Download PDFInfo
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Abstract
The invention discloses a system and a method for measuring a refractive index spectrum of an optical material based on phase detection. The invention utilizes a frequency-sweeping optical coherence tomography system with a Mach-Zehnder interference structure to collect interference spectrum signals, and obtains phase distribution through Hilbert conversion; the continuous refractive index spectrum distribution of the sample in a wide spectrum range is obtained by detecting the phase change caused by the sample and utilizing the theoretical formula provided by the invention; and resampling the phase change caused by the sample by using the wavelength linear distribution resampling vector to obtain a refractive index spectrum along with the wavelength linear distribution. The principle of the invention is simple, and the system has miniaturization potential, so that the system can be used as a useful tool for measuring the refractive index and is suitable for special occasions.
Description
Technical Field
The invention relates to a technology for measuring the refractive index of an optical material, in particular to a system and a method for measuring the refractive index spectrum of the optical material by adopting a phase detection mode.
Background
Refractive Index (RI) is a fundamental parameter inherent to optical materials, and changes with λ form a Refractive Index Spectrum (RIS) distribution. The RIS information of the material can not be separated by predicting the deformation of the ultrashort laser pulse when the ultrashort laser pulse is transmitted in the material, researching the birefringence phenomenon of the crystal, designing an optical system, carrying out dispersion treatment on the material and the like. For known types of optical materials, the RIS distribution and RI values at any lambda in the spectral range from near UV to 2.3 μm can be determined by finding the dispersion coefficientAnd using a dispersion equation to obtain, for example: using Sellmeier dispersion equation and dispersion coefficient B1、B2、B3、C1、C2And C3To obtain the final product. However, the current RI measurement is only performed for specific spectral lines, for example: f (486.1nm), C (656.3nm), d (587.6nm) spectral lines, and the like. Taking schottky product data as an example, there are relatively many (17) measurement points in the ultraviolet and visible bands, and there are only a few (6) measurement points in the broader near-infrared band, such as: in the short-wave near-infrared region widely used in the biomedical field and the like, there are only 4 measurement points: 852.1nm (s line), 1014.0nm (t line), 1060nm and 1529.6 nm. In addition, the method requires that the light source can provide accurate characteristic spectral lines, and multiple light sources are needed for multiple measurements (usually, one light source can only provide one spectral line), so that the requirements on the light source are extremely high, the operation is complex, and the cost is high. If a continuous broad spectrum light source could be used instead of a single spectral line light source for RI measurement and RIs information could be obtained that approximates a continuous lambda distribution, this would help to simplify operation, improve measurement accuracy, and reduce cost.
Take the method listed on the schottky product catalog as an example: the RI of common spectral lines, such as i, h,.. r, t spectral lines and the like, is measured by a V-block refractometer; and measuring RI in the spectral range of 185-2325 nm by using a prism spectrometer. In the former, a sample material is placed on a V-shaped refractive material (the RI of which is known and needs to be larger than that of a sample to be measured), and the direction of an incident spectral line is adjusted to a critical angle thetacSo that the light can generate total reflection at the interface of the two materials, i.e. the formula n can be useds＝sin(θc)·nvTo calculate the RI of the sample, wherein: n isvAnd nsRespectively, the RI of the V-refractometer and the sample material. The latter works based on the principle of a refraction prism, and a sample needs to be processed into a prism to be used as the refraction prism, and the refraction angle of the prism is alpha; the spectral components are dispersed by the dispersion characteristics of a refractive prism by measuring the minimum deviation angle delta of the outgoing light relative to the incoming lightmdObtaining RI of each spectral component, and the calculation formula is sin [ (alpha + delta)md)/2]＝nsSin (. alpha./2). Two of the aboveThe method has extremely high requirements on the precision of angle adjustment, processing and measurement. For example, the RI accuracy of a Schottky product is 10-5Order of magnitude, which requires an angular accuracy of about 0.8 x 10 for the previous method-5Radian (about 0.03 arc-second), the requirement for the latter method is about 1.5X 10-5Radian (about 0.05 arc seconds), are very demanding. Therefore, finding a measuring method which is simpler and easier to operate would be helpful to improve the measuring efficiency and ensure the measuring accuracy.
In many cases, the type of material used for the optical device is unknown, and can be inferred by measuring the intrinsic parameter RI. However, the RI values of different materials are relatively close, and the type of the material cannot be judged sufficiently only by measuring RI of a single lambda or a small number of lambda. If the RIS information distributed along with the lambda can be obtained and the dispersion coefficient is further obtained by fitting the dispersion equation, different optical materials can be fully distinguished, and the type of the optical material can be judged by comparing the obtained dispersion coefficient with the standard dispersion coefficient in the material library. This puts a demand on the measurement of RIS, an optical material.
Optical Coherence Tomography (OCT) techniques have been reported for RI measurements including Optical samples, turbid media, biological tissues, small animal tissues, and human skin tissues and human lenses. However, all these works can only obtain the average RI value of the sample, and no report of OCT for continuous λ distribution RIS measurement is available. OCT uses broadband, even ultra-wideband light source formed by splicing multiple light sources to measure, and provides possibility for continuous RIS measurement in a wide spectral range. The RI of the optical material is obtained by phase detection, but the requirements of phase detection on device and environmental stability are extremely high. Compared with spectral domain OCT, the swept frequency OCT can adopt an optical fiber type device, and the sweep frequency rate of a swept frequency light source is extremely high, so that signals can be rapidly collected, and the interference of unstable factors on measurement results can be avoided or reduced. In addition, in the commonly used short-wave near-infrared regions of 800, 1000 and 1300nm wave bands and the like, sweep frequency light sources with the bandwidth exceeding 100nm and corresponding detector products are available at present. Therefore, the swept frequency OCT is more advantageous to improve stability.
Optical devices used in optical systems are almost always coated with a film layer, such as an antireflection film, to reduce the stray light signal reflected from the interface. The film layer can cause phase changes and cause thickness measurement inaccuracies, thereby affecting the measurement results. Therefore, it is a reasonable solution to measure RI using an optical material without a coating film as a sample. However, uncoated optics typically present strong interfacial reflected light signals that can be collected and form a harmful strong background and self-coherent signal in typical reflective OCT systems. Although placing the sample surface non-perpendicular to the incident light avoids this problem, the optical path measurement becomes complex and difficult to measure accurately. The mach-zehnder interference structure is an effective way to solve the above problem, and only receives the optical signal transmitted through the sample without being interfered by the back reflected optical signal at the sample interface.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the defects of the prior art are overcome, and a system and a method for measuring continuous RIS distribution in a wide spectral range are provided. Acquiring interference spectrum signals by using a frequency-sweeping OCT system with a Mach-Zehnder interference structure, and acquiring phase information by virtue of Hilbert conversion; the RIS distribution of the sample is obtained by measuring the phase change caused by the sample and utilizing the theoretical formula provided by the invention; it is also necessary to obtain a resampling vector of the linear λ distribution, and to resample the phase change distribution caused by the sample using the resampling vector to obtain RIS information that changes with the linear λ distribution.
The technical scheme adopted by the invention for solving the technical problems is as follows: an optical material refractive index spectrum measurement system based on phase detection is disclosed, which comprises: the device comprises a sweep frequency light source, a first optical fiber coupler, a first transmission type collimator, a second transmission type collimator, a translation table, a first reflection type collimator, a second reflection type collimator, a first polarization controller, a second optical fiber coupler, a balance detector, a digital oscilloscope, a computer, a sample, an optical fiber and a signal line;
after optical signals sent by the sweep frequency light source are transmitted by optical fibers, the optical signals are divided into two paths by the first optical fiber coupler and respectively enter the reference arm and the sample arm; the optical signals entering the reference arm and the sample arm are respectively collimated by the first transmission collimator and the second transmission collimator, then respectively received by the first reflection collimator and the second reflection collimator, and finally transmitted to the balance detector through the second optical fiber coupler; the balance detector converts the received optical signal into an analog electrical signal and transmits the analog electrical signal to the digital oscilloscope for display through a signal wire; the digital oscilloscope converts the analog electric signal into a digital signal and transmits the digital signal to a computer for processing;
the second transmission type collimator is fixed on the translation table, the sample is arranged between the second transmission type collimator and the second reflection type collimator, the first polarization controller and the second polarization controller are installed on an input end optical fiber of the second optical fiber coupler, and scanning synchronous trigger signals output by the sweep frequency light source are transmitted to the digital oscilloscope through signal lines.
Further, the translation stage drives the second transmission collimator to move to adjust the optical path difference between the reference arm and the sample arm, so that interference fringes appear on the digital oscilloscope; the signal of the interference fringe is strongest and regular in shape by adjusting the first polarization controller and the second polarization controller.
According to another aspect of the present invention, a method for measuring a refractive index spectrum of an optical material based on phase detection is provided, which comprises the following steps:
step 1: acquiring a resampling vector of wavelength lambda linear distribution;
step 2: acquiring the phase distribution of a sample;
and step 3: calculating the refractive index spectrum n (lambda) distribution of the sample;
and 4, step 4: and (3) comparing with a standard refractive index spectrum n (lambda) curve in a material library to judge the type of the sample.
Further, the step 1 specifically includes:
step 11: the second transmissive collimator is moved to an optical path difference Δ z1At the initial position, interference spectrum signals I are collected by a balance detector (11)1(lambda) and calculating the phase theta by using the expressions (3) and (4)1(λ); the method comprises the following specific steps:
the interference spectral signal I (λ) acquired by the balanced detector (11) is expressed as:
in the formula: λ is wavelength and its range is λ1～λ2；Ir(lambda) and Is(λ) is the incoherent signal from the reference and sample arms, which constitutes the background signal; t is the transmittance of the sample; Δ z is the optical path difference between the reference arm and the sample arm; Γ (Δ z) is the coherence function of the swept source output instantaneous λ; thetadm(λ) is the phase due to dispersion mismatch between the reference and sample arms; the third term is a mutual interference signal formed by optical signals between the reference arm and the sample arm, and for a given Δ z, the part in front of the cosine function is a constant and is marked as C; after subtracting the background signal, I (λ) represented by formula (1) is reduced to interference spectrum signal I' (λ) represented by formula (2):
I′(λ)＝Ccos[(2π/λ)Δz+θdm(λ)]， (2)
the phase θ (λ) of I '(λ) is obtained by the arctan operation from the hilbert transform result of I' (λ) and itself; however, the phase obtained is wrapped between-pi/2 and pi/2, and the unwrapping process is required to obtain the unwrapped phase θ' (λ):
θ′(λ)＝unwrapping{arctan[HT(I′(λ))/I′(λ)]}， (3)
in the formula: HT, arctan, and unwraping, which represent hilbert transform, arctangent, and phase unwrapping processes, respectively; by (2 π/λ)2) Δ z corrects θ' (λ) to obtain the true θ (λ):
θ(λ)＝(2π/λ)Δz+θdm(λ)＝θ′(λ)+(2π/λ2)Δz， (4)
smoothing theta (lambda) to eliminate burrs;
step 12: the second transmission collimator moves to a distance d away from the second reflection collimator, and the optical path difference is delta z2＝Δz1+ d, collecting interference spectrum signal by balance detectorI2(lambda) and calculating the phase theta by using the expressions (3) and (4)2(λ)；
Step 13: the phase change Δ θ caused when the optical path difference changes d is calculated by the equation (5)21(λ)＝θ2(λ)-θ1(λ); the method comprises the following specific steps:
the second transmissive collimator is moved to an optical path difference Δ z1At the initial position, interference spectrum signals I are collected by a balance detector (11)1(lambda) and calculating the phase theta by using the expressions (3) and (4)1(λ); the second transmission collimator moves a distance d away from the second reflection collimator, and the optical path difference is Δ z2＝Δz1+ d, collecting interference spectrum signal I by balance detector (11)2(lambda) and calculating the phase theta by using the expressions (3) and (4)2(λ); the phase change Δ θ caused when the optical path difference changes d21(λ)＝θ2(λ)-θ1(λ) is:
Δθ21(λ)＝(2π/λ)d＝[θ2′(λ)-θ1′(λ)]+(2π/λ2)d， (5)
phase theta caused by dispersion mismatch by phase subtractiondm(λ) has been eliminated;
step 14: obtaining a resampling vector by using the formula (6); the method comprises the following specific steps:
the λ linear distribution resample vector obtained from equation (5) is expressed as:
further, the step 2 of obtaining the phase distribution of the sample specifically includes:
step 21: the second transmission collimator returns to the initial position, and a sample with refractive index n (lambda) and thickness t is put in the second transmission collimator, and the optical path difference is delta z3＝Δz1+t[n(λ)-1]Acquisition of interference spectral signals I by a balanced detector3(lambda) and calculating the phase theta by using the expressions (3) and (4)3(λ)；
Step 22: calculating the optical path difference change t [ n ] using equation (7)(λ)-1]Time, induced phase change Δ θ31(λ)＝θ3(λ)-θ1(λ)：
Δθ31(λ)＝(2π/λ)[t(n(λ)-1)]＝[θ3′(λ)-θ1′(λ)]+(2π/λ2)[t(n(λ)-1)]。 (7)
Further, the step 3 calculates a refractive index spectrum n (λ) distribution of the sample according to formula (8); the method comprises the following specific steps:
the refractive index spectrum n (λ) distribution of the sample obtained from equation (7) is:
wherein: theta3′(λ)-θ1' (lambda) lambda linear distribution resampling processing is carried out on the resampling vector obtained by the formula (6);
the Sellmeier dispersion equation is used for the calculation of the theoretical n (lambda) of an optical material, and the expression is as follows:
in the formula: b is1、B2、B3、C1、C2、C3Is the dispersion coefficient; when n (λ) is calculated using the dispersion coefficients in the schottky database, λ is in microns.
Compared with the prior art, the invention has the beneficial effects that:
1) the invention can obtain continuous RIS information of optical material in wide spectrum range, not discrete RI information measured only by characteristic spectral line, nor average RI information obtained by current OCT technique for RI measurement. RIS, an optical material, is indispensable information for many fields.
2) The invention obtains the RIS of the sample by measuring the phase change caused by the change of the optical path difference, and avoids the absolute measurement of parameters such as the optical path, the phase and the like. Absolute measurements usually require extremely high measurement accuracy, or require complicated calibration, etc.
3) The invention eliminates the phase interference caused by optical system dispersion mismatch through phase subtraction. This phase can be aliased with the phase induced by the sample, resulting in erroneous measurements, and therefore is usually eliminated by physical and/or software dispersion balancing, but these methods are complicated.
4) The working principle, the measuring system, the experimental method, the data processing and the like of the invention are simple. In particular, the measuring system has the potential of realizing miniaturization and portability, so that the measuring system is suitable for special occasions such as field, optical processing field, large-scale optical system on-line measurement and the like.
Drawings
FIG. 1 is a schematic diagram of the system architecture of the present invention;
FIG. 2 is a flow chart of a phase extraction method employed in the present invention;
FIG. 3 is a schematic diagram of the measurement operation and signal acquisition of the present invention;
FIG. 4 is a flow chart of a method of the present invention;
FIG. 5 is a diagram illustrating the results of the main process for generating wavelength linear profile resampling vectors: (a1) is an interference spectral signal I1(λ); (a2) is the phase theta1'; (b1) is an interference spectral signal I2(λ); (b2) is the phase theta2'; (c) is the phase difference Delta theta2′1(ii) a (d) Is a resampled vector;
FIG. 6 is an exemplary graph of the main process results of refractive index spectroscopy measurement of N-BK7 material: (a) is an interference spectral signal I3(λ); (b) is the phase theta3'; (c) is the phase difference Delta theta3′1(ii) a (d) Is a phase difference Δ θ with respect to λ3′1(λ); (e) is a refractive index spectrum;
FIG. 7 is a certain refractive index spectrum measurement of the N-LAK22 and N-BK7 materials: (a) is the refractive index spectrum of N-LAK 22; (b) is the refractive index spectrum of N-BK 7.
In the figure: 1. the system comprises a sweep light source, 2, a first optical fiber coupler, 3, a first transmission type collimator, 4, a second transmission type collimator, 5, a translation table, 6, a first reflection type collimator, 7, a second reflection type collimator, 8, a first polarization controller, 9, a second polarization controller, 10, a second optical fiber coupler, 11, a balance detector, 12, a digital oscilloscope, 13, a computer, 14, a sample, 15, an optical fiber and 16, signal lines.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments, and all other embodiments obtained by a person skilled in the art based on the embodiments of the present invention belong to the protection scope of the present invention without creative efforts.
As shown in fig. 1, the optical material refractive index spectrum measurement system based on phase detection provided by the present invention is a swept frequency OCT system based on a mach-zehnder interference structure, and includes a swept frequency light source 1, a first optical fiber coupler 2, a first transmissive collimator 3, a second transmissive collimator 4, a translation stage 5, a first reflective collimator 6, a second reflective collimator 7, a first polarization controller 8, a second polarization controller 9, a second optical fiber coupler 10, a balance detector 11, a digital oscilloscope 12, a computer 13, a sample 14, an optical fiber 15, and a signal line 16.
After being transmitted by the optical fiber 15, the optical signal emitted by the swept-frequency light source 1 is divided into two paths by the first optical fiber coupler 2, and the two paths respectively enter the reference arm and the sample arm. The optical signals entering the reference arm and the sample arm are respectively collimated by the first transmission collimator 3 and the second transmission collimator 4, then respectively received by the first reflection collimator 6 and the second reflection collimator 7, and finally transmitted to the balanced detector 11 through the second optical fiber coupler 10. The balance detector 11 converts the received optical signal into an analog electrical signal, and transmits the analog electrical signal to the digital oscilloscope 12 through the signal wire 16 for displaying; the digital oscilloscope 12 converts the analog electrical signal into a digital signal, and transmits the digital signal to the computer 13 for processing.
The second transmission type collimator 4 is fixed on the translation stage 5, the sample 14 is arranged between the second transmission type collimator 4 and the second reflection type collimator 7, the first polarization controller 8 and the second polarization controller 9 are installed on the input end optical fiber of the second optical fiber coupler 10, and the scanning synchronous trigger signal output by the sweep frequency light source 1 is transmitted to the digital oscilloscope 12 through the signal line 16. The translation stage 5 moves with the second transmission collimator 4 to adjust the optical path difference between the reference arm and the sample arm, so that interference fringes appear on the digital oscilloscope 12. The signal of the interference fringes is made strongest and regular in shape by adjusting the first polarization controller 8 and the second polarization controller 9.
The invention provides a phase detection-based optical material refractive index spectrum measurement method, which utilizes the system to measure, and specifically comprises the following steps:
the interference spectrum signal I (λ) collected by the balanced detector 11 can be expressed as:
in the formula: λ is wavelength and its range is λ1～λ2；Ir(lambda) and Is(λ) are the incoherent signals from the reference and sample arms, respectively, which constitute the background signal; t is the transmittance of sample 14; Δ z is the optical path difference between the reference arm and the sample arm; Γ (Δ z) is the coherence function of the instantaneous λ output by the swept-frequency light source 1; thetadm(λ) is the phase due to dispersion mismatch between the reference and sample arms; the third term is a mutual interference signal formed by optical signals between the reference arm and the sample arm, and for a given Δ z, the part in front of the cosine function is a constant and is marked as C; after subtracting the background signal, I (λ) represented by formula (1) is reduced to interference spectrum signal I' (λ) represented by formula (2):
I′(λ)＝Ccos[(2π/λ)Δz+θdm(λ)]， (2)
the phase is extracted using a workflow as shown in fig. 2. The phase θ (λ) of I '(λ) can be obtained by the inverse tangent operation from the hilbert transform result of I' (λ) and itself. However, the phase obtained is wrapped between-pi/2 and pi/2, and the unwrapping process is required to obtain the unwrapped phase θ' (λ):
θ′(λ)＝unwrapping{arctan[HT(I′(λ))/I′(λ)]}， (3)
in the formula: HT, arctan, and unwraping, which represent hilbert transform, arctangent, and phase unwrapping processes, respectively. By (2 π/λ)2) Δ z corrects θ' (λ) to obtain the true θ (λ):
θ(λ)＝(2π/λ)Δz+θdm(λ)＝θ′(λ)+(2π/λ2)Δz， (4)
the smoothing process is performed on θ (λ) to remove the glitch, and the existence of the glitch may cause failure of subsequent processes.
The instantaneous λ output by the swept-source 1 is a nonlinear distribution, and the interference spectrum signal I (λ) collected by the balanced detector 11 is also a function of the nonlinear distribution λ. RIS is a function of a linear distribution λ, which is more convenient to use and more customary. Therefore, it is necessary to obtain a resampling vector of λ linear distribution, then perform linear λ resampling processing on the obtained phase distribution, and finally obtain RIS information of λ linear distribution from the resampling phase.
The measurement operation and signal acquisition process of the present invention is shown in fig. 3. The second transmissive collimator 4 is moved to an optical path difference Δ z1At an initial position, interference spectrum signals I are collected by a balance detector 111(lambda) and calculating the phase theta by using the expressions (3) and (4)1(lambda). The second transmissive collimator 4 moves a distance d away from the second reflective collimator 7, and the optical path difference is Δ z2＝Δz1+ d, acquisition of the interference spectrum signal I by the balanced detector 112(lambda) and calculating the phase theta by using the expressions (3) and (4)2(lambda). The phase change Δ θ caused when the optical path difference changes d21(λ)＝θ2(λ)-θ1(λ) is:
Δθ21(λ)＝(2π/λ)d＝[θ2′(λ)-θ1′(λ)]+(2π/λ2)d， (5)
phase theta caused by dispersion mismatch by phase subtractiondm(λ) has been eliminated. The λ linear distribution resample vector obtained from equation (5) can be expressed as:
the second transmission collimator 4 returns to the initial position, and the sample 14 having an RIS of n (λ) and a thickness t is put therein with an optical path difference Δ z3＝Δz1+t[n(λ)-1]The interference spectrum signal I is collected by the balance detector 113(lambda) and calculating the phase theta by using the expressions (3) and (4)3(lambda). The optical path difference is changed by t [ n (λ) -1]Time, induced phase change Δ θ31(λ)＝θ3(λ)-θ1(λ) is:
Δθ31(λ)＝(2π/λ)[t(n(λ)-1)]＝[θ3′(λ)-θ1′(λ)]+(2π/λ2)[t(n(λ)-1)]， (7)
the RIS distribution of sample 14 obtained from formula (7) is:
wherein: theta3′(λ)-θ1' (λ) requires λ linear distribution resampling processing by the resampling vector obtained by equation (6).
The Sellmeier dispersion equation is used for the calculation of the theoretical n (lambda) of an optical material, and the expression is as follows:
in the formula: b is1、B2、B3、C1、C2、C3Is the dispersion coefficient; when n (λ) is calculated using the dispersion coefficients in the schottky database, λ is in microns.
As shown in fig. 4, the method for measuring refractive index spectrum of optical material based on phase detection in the present invention includes the following steps:
step 1: acquiring a resampling vector of wavelength lambda linear distribution;
step 11: the second transmissive collimator 4 is moved to an optical path difference Δ z1At an initial position of the interference is collected by the balanced detector 11Spectral signal I1(lambda) and calculating the phase theta by using the expressions (3) and (4)1(λ)；
Step 12: the second transmissive collimator 4 is moved in a direction away from the second reflective collimator 7 by a distance d, and the optical path difference is Δ z2＝Δz1+ d, acquisition of the interference spectrum signal I by the balanced detector 112(lambda) and calculating the phase theta by using the expressions (3) and (4)2(λ)；
Step 13: the phase change Δ θ caused when the optical path difference changes d is calculated by the equation (5)21(λ)＝θ2(λ)-θ1(λ)；
Step 14: obtaining a resampling vector by using the formula (6);
step 2: acquiring a phase profile of the sample 14;
step 21: the second transmissive collimator 4 returns to the initial position, and the sample 14 having the refractive index n (λ) and the thickness t is put therein with the optical path difference Δ z3＝Δz1+t[n(λ)-1]The interference spectrum signal I is collected by the balance detector 113(lambda) and calculating the phase theta by using the expressions (3) and (4)3(λ)；
Step 22: calculating the optical path difference change t [ n (λ) -1 by using the formula (7)]Time, induced phase change Δ θ31(λ)＝θ3(λ)-θ1(λ)；
And step 3: calculating a refractive index spectrum n (λ) distribution of the sample 14 using equation (8);
and 4, step 4: the material type of the sample 14 is judged by comparison with a standard refractive index spectrum n (λ) distribution in a material library.
As an example, the following method utilizes a sweep light source with 1300nm waveband of Axsun corporation, USA, sweep rate of 50kHz and lambda range of 1259-1366 nm to perform RIS measurement on two optical materials of N-LAK22 and N-BK 7. The geometrical thicknesses t of the two optical materials were 4.5mm and 1.1mm, respectively, and the dispersion coefficients are shown in Table 1, and their theoretical RIS distributions were obtained by using formula (9).
TABLE 1 Sellmeier Dispersion equation Dispersion coefficients for the two materials.
Fig. 5 is a result of some of the main processes for generating a lambda linear distribution resample vector. At an optical path difference of Δ z1(without knowing specific values), the interference spectrum signal I collected by the balanced detector 111(lambda) and phase theta calculated by using the formulas (3) and (4)1' (λ) as shown in FIGS. 5(a1) and 5(a2), respectively. At an optical path difference of Δ z2＝Δz1+ d (in this example, d is 0.5mm), the interference spectrum signal I collected by the balance detector 112(lambda) and phase theta calculated by using the formulas (3) and (4)2' (λ) as shown in FIGS. 5(b1) and 5(b2), respectively. Phase difference Δ θ in formula (6)2′1(λ)＝θ2′(λ)-θ1' (λ) is shown in FIG. 5 (c). The resampling vector calculated by equation (6) shows that the resampling pitch of λ is 0.1nm as shown in fig. 5(d), but the circle in the figure shows the display at intervals of 10 sampling points, that is, when the λ pitch is 1 nm.
FIG. 6 shows the main process results of RIS measurement using N-BK7 material as an example. At an optical path difference of Δ z3＝Δz1+t[n(λ)-1]While, the interference spectrum signal I collected by the balance detector 113(lambda) and phase theta calculated by using the formulas (3) and (4)3' (λ) as shown in FIGS. 6(a) and 6(b), respectively. Phase difference Δ θ in formula (8)3′1(λ)＝θ3′(λ)-θ1' (λ) is shown in FIG. 6(c), here as a function of the sampling point, and the result of linearly λ resampling it with the resampling vector is shown as a circle in the figure. By taking the resampling point of linear lambda distribution as a transition bridge, lambda and delta theta can be measured3′1(λ) are connected, and the result shown in FIG. 6(d) is obtained. Linearly distributed λ and corresponding Δ θ3′1(λ) was substituted in formula (8) to obtain the RIS measurement result shown in fig. 6 (e). The denominator in formula (8) has λ2-a term of λ, when λ is close to λ2The denominator will tend to zero, Δ θ in the numerator3′1(λ) is also close to zero, resulting in large variations or uncertainties in the RIS of the area. Therefore, on the right side in FIG. 6(e)(close to λ)2Where) a large RI change occurs, which is not correct, so that a small portion of the data in the region needs to be discarded, and only a large portion of the data in the middle normal region is used. The area indicated by the dashed line box is enlarged and displayed, and the result is shown in the inset in fig. 6(e), and it can be seen from the figure that: the experimental curve is closer to the theoretical curve in the lambda range of about 100 nm.
For the two optical materials N-LAK22 and N-BK7, 5 independent experiments were performed to measure their RIS distribution, one of which is shown in FIG. 7. The measured and theoretical values at the fraction λ for the two materials are listed in table 2 for comparison, where: the measured value is the average value and the standard deviation of 5 measurement results; the relative error is expressed in percentage and the calculation formula is (RI)meas.-RItheo.)/RItheo.Wherein: RI (Ri)meas.And RItheo.Respectively representing measured and theoretical values of RI. It can be seen that: the relative error is small, the measured values and the theoretical values of the two materials are relatively consistent, and the feasibility of the invention is verified.
Table 2 refractive index spectra measurements (mean ± standard deviation of 5 measurements) and theoretical values at some wavelengths for both materials.
Claims (6)
1. An optical material refractive index spectrum measurement system based on phase detection is characterized in that: the device comprises a sweep frequency light source (1), a first optical fiber coupler (2), a first transmission type collimator (3), a second transmission type collimator (4), a translation table (5), a first reflection type collimator (6), a second reflection type collimator (7), a first polarization controller (8), a second polarization controller (9), a second optical fiber coupler (10), a balance detector (11), a digital oscilloscope (12), a computer (13), a sample (14), an optical fiber (15) and a signal line (16);
after being transmitted by an optical fiber (15), an optical signal emitted by the sweep frequency light source (1) is divided into two paths by the first optical fiber coupler (2) and respectively enters the reference arm and the sample arm; after being collimated by a first transmission collimator (3) and a second transmission collimator (4), optical signals entering a reference arm and a sample arm are respectively received by a first reflection collimator (6) and a second reflection collimator (7), and are finally transmitted to a balance detector (11) through a second optical fiber coupler (10); the balance detector (11) converts the received optical signal into an analog electrical signal, and transmits the analog electrical signal to the digital oscilloscope (12) through a signal line (16) for displaying; the digital oscilloscope (12) converts the analog electric signal into a digital signal and transmits the digital signal to the computer (13) for processing;
the second transmission type collimator (4) is fixed on the translation table (5), the sample (14) is arranged between the second transmission type collimator (4) and the second reflection type collimator (7), the first polarization controller (8) and the second polarization controller (9) are installed on an input end optical fiber of the second optical fiber coupler (10), and scanning synchronous trigger signals output by the sweep frequency light source (1) are transmitted to the digital oscilloscope (12) through a signal line (16).
2. The system of claim 1, wherein the system comprises: the translation stage (5) drives the second transmission collimator (4) to move to adjust the optical path difference between the reference arm and the sample arm, so that interference fringes appear on the digital oscilloscope (12); the signal of the interference fringes is strongest and regular in shape by adjusting the first polarization controller (8) and the second polarization controller (9).
3. A method for measuring refractive index spectra of optical materials based on phase detection using the system of any one of claims 1-2, comprising the steps of:
step 1: acquiring a resampling vector of wavelength lambda linear distribution;
step 2: acquiring the phase distribution of a sample;
and step 3: calculating the refractive index spectrum n (lambda) distribution of the sample;
and 4, step 4: and (3) comparing with a standard refractive index spectrum n (lambda) curve in a material library to judge the type of the sample.
4. The method for measuring the refractive index spectrum of the optical material based on the phase detection as claimed in claim 3, wherein the step 1 specifically comprises:
step 11: the second transmissive collimator (4) is moved to an optical path difference Δ z1At the initial position, interference spectrum signals I are collected by a balance detector (11)1(lambda) and calculating the phase theta by using the expressions (3) and (4)1(λ); the method comprises the following specific steps:
the interference spectral signal I (λ) acquired by the balanced detector (11) is expressed as:
in the formula: λ is wavelength and its range is λ1～λ2；Ir(lambda) and Is(λ) is the incoherent signal from the reference and sample arms, which constitutes the background signal; t is the transmittance of the sample (14); Δ z is the optical path difference between the reference arm and the sample arm; Γ (Δ z) is a coherence function of the instantaneous λ output by the swept-frequency light source (1); thetadm(λ) is the phase due to dispersion mismatch between the reference and sample arms; the third term is a mutual interference signal formed by optical signals between the reference arm and the sample arm, and for a given Δ z, the part in front of the cosine function is a constant and is marked as C; after subtracting the background signal, I (λ) represented by formula (1) is reduced to interference spectrum signal I' (λ) represented by formula (2):
I′(λ)＝C cos[(2π/λ)Δz+θdm(λ)]， (2)
the phase θ (λ) of I '(λ) is obtained by the arctan operation from the hilbert transform result of I' (λ) and itself; however, the phase obtained is wrapped between-pi/2 and pi/2, and the unwrapping process is required to obtain the unwrapped phase θ' (λ):
θ′(λ)＝unwrapping{arctan[HT(I′(λ))/I′(λ)]}， (3)
in the formula: HT, arctan, and unwraping, which represent hilbert transform, arctangent, and phase unwrapping processes, respectively; by (2 π/λ)2) Δ z corrects θ' (λ) to obtain the true θ (λ):
θ(λ)＝(2π/λ)Δz+θdm(λ)＝θ′(λ)+(2π/λ2)Δz， (4)
smoothing theta (lambda) to eliminate burrs;
step 12: the second transmission collimator (4) moves to a distance d away from the second reflection collimator (7), and the optical path difference is delta z2＝Δz1+ d, collecting interference spectrum signal I by balance detector (11)2(lambda) and calculating the phase theta by using the expressions (3) and (4)2(λ)；
Step 13: the phase change Δ θ caused when the optical path difference changes d is calculated by the equation (5)21(λ)＝θ2(λ)-θ1(λ); the method comprises the following specific steps:
the second transmissive collimator (4) is moved to an optical path difference Δ z1At the initial position, interference spectrum signals I are collected by a balance detector (11)1(lambda) and calculating the phase theta by using the expressions (3) and (4)1(λ); the second transmission collimator (4) moves to a direction far away from the second reflection collimator (7) by a distance d, and the optical path difference is delta z2＝Δz1+ d, collecting interference spectrum signal I by balance detector (11)2(lambda) and calculating the phase theta by using the expressions (3) and (4)2(λ); the phase change Δ θ caused when the optical path difference changes d21(λ)＝θ2(λ)-θ1(λ) is:
Δθ21(λ)＝(2π/λ)d＝[θ′2(λ)-θ′1(λ)]+(2π/λ2)d， (5)
phase theta caused by dispersion mismatch by phase subtractiondm(λ) has been eliminated;
step 14: obtaining a resampling vector by using the formula (6); the method comprises the following specific steps:
the λ linear distribution resample vector obtained from equation (5) is expressed as:
5. the method according to claim 3, wherein the step 2 of obtaining the phase distribution of the sample specifically comprises:
step 21: the second transmission collimator (4) returns to the initial position, and a sample (14) having a refractive index n (λ) and a thickness t is placed therein with an optical path difference Δ z3＝Δz1+t[n(λ)-1]The interference spectrum signal I is collected by a balance detector (11)3(lambda) and calculating the phase theta by using the expressions (3) and (4)3(λ)；
Step 22: calculating the optical path difference change t [ n (λ) -1 by using the formula (7)]Time, induced phase change Δ θ31(λ)＝θ3(λ)-θ1(λ)：
Δθ31(λ)＝(2π/λ)[t(n(λ)-1)]＝[θ′3(λ)-θ′1(λ)]+(2π/λ2)[t(n(λ)-1)]。 (7)
6. A method for measuring the refractive index spectrum of an optical material based on phase detection according to claim 3, wherein the step 3 calculates the refractive index spectrum n (λ) distribution of the sample (14) according to the formula (8); the method comprises the following specific steps:
the refractive index spectrum n (λ) distribution of the sample (14) obtained from equation (7) is:
wherein: theta'3(λ)-θ′1(λ) performing λ linear distributed resampling processing on the resample vector obtained by the formula (6);
the Sellmeier dispersion equation is used for the calculation of the theoretical n (lambda) of an optical material, and the expression is as follows:
in the formula: b is1、B2、B3、C1、C2、C3Is the dispersion coefficient; when n (λ) is calculated using the dispersion coefficients in the schottky database, λ is in microns.
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