Patent Application
20220221767
The present invention relates to a method for controlling an optical deflector and an optical deflection device.
Optical deflection units that change the direction of travel of light by applying an alternating voltage such as a sine wave to a dielectric (electro-optical material) in a paraelectric phase are used in various fields such as laser printers, wavelength sweep light sources, and the like. For example, a wavelength sweep light source in which an electro-optical crystal in a paraelectric phase (dielectric crystal of a paraelectric phase) is disposed in an optical resonator has been proposed (see PTL 1). The wavelength sweep light source superimposes a DC voltage to fill a trap in electro-optical crystals with electrons as a bias voltage in applying an AC voltage for fast deflection to the electro-optical crystal. The wavelength sweep light source configured in this manner can suppress fluctuations in the light output, the sweep wavelength band, and the coherence length over an extended period of time, and has excellent long-term stability.
Techniques have been proposed for applying an AC drive voltage in which a DC voltage is superimposed as a bias voltage while irradiating the electro-optical crystal with light from an optical irradiation unit (see PTL 2). In this proposal, it is believed that electron injection into the trap within the electro-optical crystal can reduce the time to reach a steady state. It is also believed that optical deflectors using electro-optical materials will also be applied in the future in laser processing and the like other than the fields described above.
KTN (KTa1-xNbxO3) or KLTN (K1-yLiyTa1-xNbxO3) having a large electro-optical effect are known as electro-optical crystals having the above-described characteristics. Hereinafter, in a case where there is no need to distinguish between KTN and KLTN, these are collectively referred to as KTN. Furthermore, in a case where Ti or Cr material is used as an electrode, the charge can be injected into the KTN, and the internal electric field generated by the injected charge can be used to achieve a high speed and wide angle optical deflector.
The graphite sheets 12a and 1213, are inserted to prevent the KTN crystal 11 from breaking due to vibration in a case of applying a high frequency control voltage to the KTN crystal it Aluminum nitrides (AlNs) 14a and 14b are inserted on both sides of the KTN crystal 11. The function of the AlNs 14a and 14b is to serve as a heat transfer member for positioning the KTN crystal 11 and for maintaining the temperature of the two metal blocks 13a and 13b uniform. A Peltier element 16 is disposed between the metal block 13a and a support plate 15, and thermistors (temperature detection units) 17a and 17b, are embedded within the metal blocks 13a and 13b, respectively.
A temperature control device 18 detects temperature by the thermistors 17a and 17b, and heats or cools the metal block 13a by the Peltier element 16 to maintain the KTN crystal 11 at the appropriate set temperature (constant temperature). The temperature control device 18 detects the temperature by measuring the resistance value of the thermistor 17a and the thermistor 17b, connected in series, and keeps the dielectric constant of the KTN crystal 11 constant.
Generally, light has an intensity distribution in a cross section perpendicular to the direction of travel, but hereinafter the centroid of this intensity distribution will be referred to as the centroid position of the light or simply the position of the light. Depending on the field of application of the optical deflector, it is required that the centroid position of the light deflected by the optical deflector have desired time dependency. For example, two optical deflectors can be connected in series to deflect the light in a circular manner. In this way, in a case of deflecting the light along a circle of radius A, the centroid position of the light deflected by each optical deflector is required to have time dependency such as x=A cos(ω+B), y=A sin(ω+B). Here, each of x and y is an orthogonal coordinate axes, ω is the angular frequency, t is the time, and B is the initial phase.
As described in Patent Literatures 1, 2, and 3, it is known to apply an AC voltage (alternating voltage) to an electro-optical crystal. However, even in a case where a sine wave voltage is applied as a voltage, it is not clear whether the time dependency of the position of the deflected light beam is represented by a sine wave (shows a simple harmonic motion).
Embodiments of the present invention are made to solve the problems described above, and an object of embodiments of the present invention is to make the position (trajectory) of light deflected by an optical deflector to have desired time dependency.
A method for controlling an optical deflector according to embodiments of the present invention is a method for controlling an optical deflector that changes a deflection angle depending on a voltage to be applied, the method for controlling the optical deflector deriving a goal voltage V=ggoal(t) for providing a deflection angle θ with goal time dependency θ=θgoal(t) when time is denoted by t, the method including: an initial step in which in a case where θ is a periodic function of time, a period is denoted by T, in a case where θ is not a periodic function of time, a duration is denoted by T and a start time of the deflection angle with the goal time dependency θ=θgoal(t) is set as t=0, and when time in a period 0≤t<T is considered, the number of repetitions is set as n=0; an increment step of setting n=n+1; a step An of applying a voltage gn(t) with the period T or the duration T to the optical deflector; a step Bn of checking whether θ=θgoal(t) is satisfied with a goal accuracy, next to the step An; a step Cn of setting gn(t) as a goal voltage; a step Dn of deriving θ=frise, n(V) indicating voltage dependency of a deflection angle when a voltage applied to the optical deflector rises, and voltage dependency θ=fall, n(V) of a deflection angle when a voltage applied to the optical deflector falls; a step En of setting grise, n+1(t)=frise, n−1{θgoal(t)}, setting gfall, n+1(t)=ffall, n−1=ffall, n−1(θgoal(t)), and configuring gn+1(t) from grise, n+1(t) and gfall, n+1(t), next to the step Dn; and a step Fn of performing the increment step next to the step En, wherein the step An is subsequent to the increment step, in the step Bn, in a case where θ=θgoal(t) is not satisfied with the goal accuracy, the step Dn is performed following the step Bn, in the step Bn, in a case where θ=θgoal(t) is satisfied with the goal accuracy, the step Cn is performed following the step Bn and a process is ended, gn+1(t) is equal to grise, n+1(t) when the voltage applied to the optical deflector rises, and is equal to gfall, n+1(t) when the voltage applied to the optical deflector falls, and the voltage dependency of the deflection angle when the voltage applied to the optical deflector rises is different from the voltage dependency of the deflection angle when the voltage applied to the optical deflector falls.
In one configuration example of the method for controlling the optical deflector described above, the optical deflector is constituted of an electro-optical material with a trap in a paraelectric phase and being for accumulating charge within the material, and an optical axis of incident light on the optical deflector is set orthogonal to a direction of an electric field of the voltage applied to the optical deflector, and the voltage is applied to the optical deflector to deflect incident light incident on the optical deflector.
In one configuration example of the method for controlling the optical deflector described above, the electro-optical material is either KTN [KTa1-αNbαO3 (0<α<1)] crystals or KLTN [K1-βLiβTa1-αNbαO3 (0<α<1, 0<β<1)] crystals with lithium being added.
An optical deflection device according to embodiments of the present invention includes: an optical deflection unit configured to change a deflection angle depending on a voltage to be applied; a voltage control unit configured to apply the voltage to the optical deflection unit; and a storage unit configured to store a value of a voltage output by the voltage control unit, wherein the storage unit stores a goal voltage for providing a deflection angle with goal time dependency, and the goal voltage is determined by the method according to claim 1.
In one configuration example of the optical deflection device described above, the optical deflector is constituted of an electro-optical material with a trap in a paraelectric phase and being for accumulating charge within the material, and an optical axis of incident light on the optical deflector is set orthogonal to a direction of an electric field of the voltage applied to the optical deflector, and the voltage is applied to the optical deflector to deflect incident light incident on the optical deflector.
In one configuration example of the optical deflection device described above, the electro-optical material is either KTN [KTa1-αNbαO3 (0<α<1)] crystals or KLTN [K1-βLiβTa1-αNbαO3 (0<α<1, 0<β<1)] crystals with lithium being added.
As described above, according to embodiments of the present invention, the step of applying gn+1(t) consisting of grise, n+1(t)=frise, n−1 (θgoal(t)), and gfall, n+1(t)=ffall, n−1 (θgoal(t)) to the optical deflector to achieve θ=θgoal(t) is repeated until θ=θgoal(t) indicating the time dependency of the deflection angle is satisfied with the goal accuracy. so that the position (trajectory) of the light deflected by the optical deflector has the desired time dependency.
Hereinafter, an optical deflection device according to an embodiment of the present invention will be described with reference to
The optical deflector 101 is composed of an electro-optical material with a trap in a paraelectric phase and being for accumulating charge within the material. The optical axis of the incident light on the optical deflector 101 is set orthogonal to the direction of the electric field of the voltage applied to the optical deflector 101. A voltage is applied to the optical deflector 101 to deflect incident light incident on the optical deflector 101. Examples of such an electro-optical material include KTN [KTa1-αNbαO3 (0<α<1)] crystals or KLTN [K1-βLiβTa1-αNbαO3 (0<α<1, 0<β<1)] crystals with lithium.
The storage unit 103 stores a goal voltage V=ggoal(t), which provides a deflection angle θ with the goal time dependency θ=θgoal(t).
Hereinafter, a method for deriving a goal voltage ggoal(t) (a method for controlling the optical deflector) stored by the storage unit 103 will be described with reference to the flowchart of
First, in step S101, the number of repetitions n=0 is set (initial step). Next, at step S102, a voltage gn(t) having a period T is applied to the optical deflector 101 (step An). Here, gn(t) is a voltage signal, e.g., “DC bias voltage+sine wave voltage” when n=0. When n≥1, gn(t) is a voltage obtained in step S106 described below.
Next, in step S103, it is confirmed whether θ=θgoal(t) is satisfied with goal accuracy (step Bn). Here, an evaluation is made whether the deflected light has a trajectory with the desired time dependency. In other words, an evaluation is made whether the deflection angle has made a desired time change represented by Equation (5) below.
The evaluation of whether the deflection angle has made the desired time change represented by Equation (5) can be achieved by a variety of methods. For example, the evaluation can be made by plotting the experimental results of the time dependency of the deflection angle on a graph and visually determining by humans from the resulting graph. The evaluation described above can be made, for example, depending on whether the maximum value of the absolute value of the difference at each time of θgoal(t) with the experimental results of the time dependency of the deflection angle is less than or equal to a desired threshold value appropriately defined. The evaluation described above can also be made, for example, depending on whether the average value of the absolute value of the difference at each time of θgoal(t) with the experimental results of the time dependency of the deflection angle is less than or equal to a desired threshold value appropriately defined.
In a case where, in step S103, θ=θgoal(t) is satisfied with the goal accuracy (yes in step S103), then in step S104, gn(t) is set to the goal voltage ggoal(t) (step Cn) and the process ends.
On the other hand, in step S103, in a case where θ=θgoal(t) is not satisfied with the goal accuracy (no in step S103), then in step S105, θ=frise, n(V) indicating the voltage dependency of the deflection angle when (during) the voltage applied to the optical deflector 101 rises and the voltage dependency θ=ffall, n(V) of the deflection angle when (during) the voltage applied to the optical deflector 101 falls are derived (step Dn). Next, in step S106, grise, n+1(t)=frise, n−1 {θgoal(t)}, and gfall, n+1(t)=ffall, n−1 (θgoal(t)) are set, and gn+1(t) is configured from grise, n+1(t) and gfall, n+1(t) (step En). Next, in step S107, n=n+1 is set as an increment step (step Fn) and the process returns to step S102. Each of the steps described above continues until θ=θgoal(t) is satisfied with the goal accuracy.
Hereinafter, more details will be described.
For example, in a case where x is required to show simple harmonic motion, h(t) can be expressed as “h(t)=x0 sin(ωt+γ)+x2 . . . (2)”. Note that in Equation (2), x0 is the amplitude, ω is the angular frequency, and γ is the initial phase. x2 is a constant, and in this case, is the central position of the simple harmonic motion. The period T is 2π/ω.
For example, in a case where x is required to show a straight trajectory at an equal speed of speed v, h(t) can be expressed as “h(t)=vt+x2 . . . (3)”. In Equation (3), x2 is a constant, and in this case, is a position at time t=0.
Meanwhile, the position at which the light beam reaches on the x-axis is determined by the incident angle θ on the optical system 104. In other words, x is a function of θ, which is expressed as x=e(θ). Then, assuming that the time dependency of the deflection angle θ that shows the desired trajectory x=h(t) is θ=θgoal(t), the equation “h(t)=e {θgoal(t)} . . . (4)” is satisfied. Solving Equation (4) inversely holds “θgoal(t)=e−1 {h(t)} . . . (5)”.
The function e may be known because it is determined by the characteristics and the arrangement of the optical components that are used. Thus, if the desired trajectory h(t) is determined, θgoal(t) is determined from Equation (5). It is not critical to select what type of optical system 104 is to be selected, and in one optical system 104, a voltage may be determined to achieve the desired deflection angle θ=θgoal(t).
Thus, as the optical system 104, a method for determining a voltage such that θ=θgoal(t) assuming the space where the distance from the pivot iota illustrated in
When the deflection angle θ of the optical deflector 101 is θ=0, the position of the transmitted light is set to x=0. By means of the optical deflector, the position of the light at which the deflection angle θ is provided can be expressed as “x=e(θ)=L tan θ . . . (6)”.
In Equation (6), in a case where θ is sufficiently small, it can be approximated as “x=e(θ)≅Lθ . . . (7)”. For example, when θ=7.5 degrees (=0.1309 rad=130.9 mrad), tan θ=0.1317, so tan θ/θ=1.006, and thus Equation (7) may be satisfied if around 0.6% of error is permitted. When θ=10 degrees (=0.1745 rad=174.5 mrad), tan θ=0.1763, so tan θ/θ=1.01, and thus Equation (7) may be satisfied if around 1% of error is permitted. When θ=15 degrees (=0.2618 rad=261.8 mrad), tan θ=0.2679, so tan θ/θ=1.02, and thus Equation (7) may be satisfied if around 2% of error is permitted. As illustrated in
Hereinafter, Equation (7) is considered to be satisfied. The deflection angle θ giving Equation (1) is θgoal(t), so by rearranging with the relationship where Equation (1) and Equation (7) are equal, θgoal(t) can be expressed as “θgoal(t)=h(t)/L . . . (8)”. Comparing Equation (5) with Equation (8), it can be seen that in this case, function e−1 is 1/L.
Consider the case where, for example, the DC bias voltage VDC+the sine wave voltage (period T) is applied as the voltage V which the voltage control unit 102 applies (outputs) to the optical deflector 101 as illustrated in
Depending on the applied conditions of the voltage, the distribution of charge injected into the electro-optical crystals may vary. In other words, the distribution of the charge at time t depends on the history of how the voltage has been applied until the time t. Thus, even if the (instantaneous) voltages are equal at VA at certain times tA and tB, the distribution of the charge at the times tA and tB is not generally said to be equal. Because the deflection angle depends on the charge distribution, θ=f(V) can be generally different at the voltage rising time θ=frise(V) and the falling time θ=ffall(V), as illustrated in
The characteristics described above are described with reference to
Here, consider the voltage waveform of the period T as illustrated in
As described above, if the voltage signal V=g(t) is provided, by measuring the deflection angle, the deflection angle θ can be expressed as a function of the instantaneous voltage V as θ=frise(V), θ=ffall(V). Thus, the deflection angle θ can be generally expressed as “θ=frise {g(t)}, θ=ffall {g(t)} . . . (9)”, as a function of the time t. Here, the domain of θ=frise {g(t)} is a time zone in which 0≤t<T and the voltage rises in time. The domain of θ=ffall {g(t)} is a time zone in which 0≤t<T and the voltage falls in time.
Suppose that when the relationship θ=frise, 0(V), θ=ffall, 0(V) derived at step Dn=0 is satisfied, voltages V exist such that the deflection angle is as Equation (8). Assuming that the voltages are denoted by grise, 1(t), gfall, 1(t), then “θgoal(t)=frise, 0 {grise, 1(t)}, θgoal(t)=ffall, 0 {gfall, 1(t)} . . . (10)” is satisfied. In other words, “grise, 1(t)=frise, 0−1 {θgoal(t)}, gfall, 1(t)=ffall, 0−1 {θgoal(t)} . . . (11)” is satisfied.
In other words, in a case of assuming that θ=frise, 0(V), θfall, 0(V) is not dependent on the history of the voltage applied, by substituting θgoal(t) of Equation (8) as θ in V=frise, 0−1(θ), V=ffall, 0−1(θ) obtained by inversely solving θ=0(V), θfall, 0(V) experimentally determined, the voltages (t) grise, 1(t), gfall, 1(t) in which x shows a trajectory with desired time dependency can be determined (step En=0).
At time 0≤t<T, a function for periodically repeating a function in which the voltage at the time of voltage rise is grise, n(t), and the voltage at the time of voltage fall is gfall, n(t) is defined as gn(t).
As previously mentioned, generally θ=f(V) depends on the history of applied voltage. However, if the history of applied voltage is similar, the shape of θ=f(V) should also be similar. Thus, by repeating the actual applying of the voltage gn+1(t) constituted by the voltages grise, n+1(t), gfall, n+1(t) obtained in step En, and the deriving of θ=frise, n+1(V), θ=ffall, n+1(V) at the next incremented step Dn+1, grise, n(t), gfall, n(t) and frise, n(t), ffall, n(t) are converged, and the deflection angle θ satisfies Equation (8), and as a result, a voltage condition in which x has the desired time dependency can be obtained. Note that, because it is not practical to repeat indefinitely (n→∞), the procedure is repeated until the θ actually indicates the desired time dependency with the desired accuracy.
The voltage g1(t) obtained at step En=0 is actually applied at the next incremented step An=1. Thereafter, at step Bn=1, an evaluation is made as to whether the time dependency of the centroid position of the deflection light is desired. In a case where the time dependency of the centroid position of the deflection light is desired, the voltage g1(t) obtained in step En=0 is the voltage signal V=ggoal(t) (Cn=1) to be determined. In a case where the time dependency of the centroid position of the deflection light is not desired, “θ=frise, 1(V), θ=ffall, 1(V)” indicating the instantaneous voltage dependency of the deflection angle θ is derived (step Dn=1). Here, suppose that there are voltages V such that the deflection angle is Equation (8) under the conditions of θ=frise, 1(V), θ=ffall, 1(V). Assuming that these are grise, 2(t), gfall, 2(t), “grise, 2(t)=frise, 1−1 {θgoal(t)}, gfall, 2(t)=ffall, 1−1 {θgoal(t)} . . . (12)” is satisfied (step En=1).
By repeating the steps described above, the voltage condition gn can be expressed as “grise, n(t)=frise, n−1−1 {θgoal(t)}, gfall, n(t)=ffall, n−1−1 {θgoal(t)} . . . (13)” (step En−1).
Hereinafter, more details will be described using examples.
First, Example 1 will be described. When the voltage illustrated in
The maximum value of the absolute value of the deflection angle represented by Equation (14) is max|±x0/L+x2/L|. For example, when x0>0, L>0, x2<0, max|±x0/L+x2/L|=|−x0/L+x2/L|. In a case where this value is sufficiently small, Equation (7) can be applied. For example, with γ=−π/2, grise, n(t), gfall, n(t) are determined by the method for controlling the optical deflector of the embodiment. The voltages grise, n(t), gfall, n(t) obtained in step En can be expressed as “grise, n(t)=frise, n−1−1 {(x0/L)sin(ωt−π/2)+x2/L}, gfall, n(t)=ffall, n−1−1 {(x0/L)sin(ωt−π/2)+x2/L} . . . (15)”, with γ=−π/2, and then substituting Equation (14) into Equation (13).
At time 0≤t<T, a function for periodically repeating a function in which the voltage at the time of voltage rise is grise, n(t), and the voltage at the time of voltage fall is gfall, n(t) is defined as gn(t), and ggoal(t)=gn(t) can be determined by repeating the procedure until θ indicates the desired time dependency with the desired accuracy. The applied voltage obtained in this way is illustrated in
Next, Example 2 is described. In Example 2 as well, when the voltage illustrated in
The deflection angle in this case can be described by the following equation substituting Equation (16) into Equation (8).
The voltages grise, n, gfall, n obtained in step En−1 can be expressed as “grise, n(t)=frise, n−−1 {(v/L)t−(vt/4L)}, gfall, n(t)=ffall, n−1−1{(v/L)t+(3vT/4L)} . . . (18)” by substituting Equation (17) into Equation (13).
At time 0≤t<T, a function for periodically repeating a function in which the voltage at the time of voltage rise is grise, n(t), and the voltage at the time of voltage fall is gfall, n(t) is defined as gn(t), and ggoal(t)=gn(t) can be determined by repeating the procedure until θ indicates the desired time dependency with the desired accuracy. The applied voltage obtained in this way is illustrated in
Note that in Example 2, the period of the voltage rise and the period of the voltage fall are both equal with the voltage T/2, but one may be longer (shorter) than the other.
If the deflection angle θ is sufficiently small, Equation (7) is satisfied, but a case in which Equation (6) is used without approximation will now be described. The deflection angle θ that satisfies Equation (1) is θgoal(t), so by rearranging with the relationship where Equation (1) and Equation (6) are equal, “θgoal(t)=tan−1 {h(t)/L} . . . (19)” is satisfied as an equation corresponding to Equation (8). Other configurations are similar to the above.
Note that, in the case of a typical optical system, Equation (5) can be used as an equation corresponding to Equation (8). Other configurations are similar to the above.
Note that the optical deflector can also be configured with an electro-optical crystal (KTN crystal) by which an optical deflection phenomenon occurs and a light irradiation unit that irradiates light to the optical crystal. Furthermore, the optical deflector is not limited to an electro-optical crystal, and the optical deflector can be configured such that the voltage dependency θ=frise(V) of the deflection angle when the voltage rises and the voltage dependency θ=ffall(V) of the deflection angle when the voltage falls are different. Although the above describes a periodic function of time as the deflection angle and voltage, when the desired deflection is started and ended after a finite period of time, without repeating periodically, the control method described with respect to the periodic function can be applied by setting the start time of the desired deflection to t=0, and the end time to t=T, with T as the duration.
As described above, according to embodiments of the present invention, the step of applying gn+1(t) consisting of grise, n+1(t)=frise, n−1 (θgoal(t)), and gfall, n+1(t)=ffall, n−1 (θgoal(t)) to the optical deflector to achieve θ=θgoal(t) is repeated until θ=θgoal(t) indicating the time dependency of the deflection angle is satisfied with the goal accuracy, so that the position (trajectory) of the light deflected by the optical deflector has the desired time dependency.
Note that, the present invention is not limited to the embodiments described above, and it is obvious that many modifications and combinations can be implemented by a person having ordinary knowledge in the field within the technical spirit of the present invention.
| Number | Date | Country | Kind |
|---|---|---|---|
| 2019-082043 | Apr 2019 | JP | national |
This application is a national phase entry of PCT Application No. PCT/JP2020/015813, filed on Apr. 8, 2020, which claims priority to Japanese Application No. 2019-082043, filed on Apr. 23, 2019, which applications are hereby incorporated herein by reference.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/JP2020/015813 | 4/8/2020 | WO | 00 |
