Probing Control Method and Apparatus for Mechanism With Multiple Degrees of Freedom

1. Field of the Invention

The present invention relates to a controlling method and apparatus for a mechanism with multiple degrees of freedom which is used in an automatic adjustment operation. More particularly, the invention is concerned with a probing control method and apparatus suitable for driving an object in such a manner that an estimation function determined from the output of the object takes the maximum value. Still more particularly, the invention is concerned with an adjusting method and apparatus suitable for use in attaining alignment of optical axes in laser diodes with optical fibers.

2. Description of the Prior Art

A laser diode with optical fiber, particularly the lens characteristics thereof, is shown in IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. QE-16, No. 10, OCTOBER 1986, pp 1059-1066, "Design of a Miniature Lens for Semiconductor Laser to Single-Mode Fiber Coupling".

In the known device of the kind described, the optical axis alignment is attained by moving the optical fiber uniaxially, i.e., with one-degree of freedom, and fixing the optical fiber at a point where the output from the fiber is maximized. With the movement of the optical fiber in one-degree of freedom, however, it is not possible to attain the true maximum output point due to, for example, lack of precision of parts, with a result that the optical axis alignment cannot be conducted with sufficiently high precision.

Accordingly, an object of the invention is to provide a probing control method which incorporates a mechanism with multiple degrees of freedom so as to move an object such as an optical fiber three-dimensionally, thereby to find out the point where the level of the output from the object is maximized.

Another object of the invention is to provide a method of controlling an automatic aligning device for optical axis alignment of a laser diode with optical fiber, capable of attaining the optical axis alignment of the fiber through detection of a point where the optical output value from the fiber is maximized.

Still another object of the invention is to provide a probing control method which is capable of diminishing the probing time and the load applied to the mechanism.

To this end, according to the invention, there is provided a method of driving, in one-by-one fashion and in accordance with a predetermined sequence, n pieces of actuators for actuating a mechanism with n-degrees of freedom, the method comprising detecting the amount of change in the output from a control object in response to the operation of said actuators, forming a command for each actuator from driving data containing the amount of movement of said actuator in the preceding operation and the amount of change in the output from the control object, and driving each actuator in accordance with the thus formed command.

FIG. 1 is a sectional view of a laser diode with an optical fiber;

FIG. 2 is an illustration of the construction of a supporting column shown in FIG. 1;

FIG. 3 is an illustration of a fine adjustment mechanism employed in the method of the invention;

FIG. 4 is a block diagram of the whole construction of an optical axis aligning apparatus to which the invention is applied;

FIGS. 5a and 5b are charts showing the result of the control;

FIG. 6 is a flow chart illustrating the controlling procedure in accordance with a first embodiment of the probing control method in accordance with the invention; and

FIG. 7 is a flow chart illustrating the control procedure in accordance with a second embodiment.

FIG. 1 shows an example of the construction of a laser diode. A reference numeral 1 denotes a laser diode chip fixed to a sub-mount 2 which is in turn secured to a frame 3. On the other hand, an optical fiber 4 passes through a hole formed in the central portion of a supporting post 5 which is fixed at its one end to frame 3. The output end is led to the outside through a hole formed in the frame 3. The position of the light-emitting portion of the laser diode chip 1 fluctuates with respect to the frame 3, due to insufficient precision of machining of the chip and insufficient precision of mounting the chip on the sub-mount. Similarly, the position of the end of the optical fiber fluctuates. In order to obtain a predetermined output from the laser diode, it is necessary that the optical axes of the laser diode chip 1 and the optical fiber 4 are aligned with a precision in the order of 0.1 .mu.m to 1 .mu.m. To this end, hitherto, the alignment has been attained by grasping one end of the supporting post 5, moving the supporting post 5 in the X and Y directions or X, Y and .theta. directions, thereby moving the end of the optical fiber 4 while plastically deforming the supporting post 5. During this operation, the output from the optical fiber 4 is observed to probe the position where the output value exceeds a predetermined level, thereby attaining optical axis alignment between the optical fiber 4 and the laser diode chip 1. In order to attain automation of this operation, it is necessary to grasp the end of the supporting post 5 by a mechanism having multiple degrees of freedom and to control the mechanism in accordance with the output from the laser diode, thereby effecting plastic deformation of the supporting post.

FIG. 3 shows a mechanism having three degrees of freedom, as an example of the mechanism with multiple degrees of freedom. This mechanism 6 has a fine adjustment device composed of an outer frame 7, intermediate frame 8, inner frame 9 and an end frame 10. The outer frame 7 and the intermediate frame 8 are coupled to each other through a parallel leaf spring mechanism. Similarly, the intermediate frame 8 and the inner frame 9 are coupled to each other through a similar parallel leaf spring mechanism. The outer frame 7 and the intermediate frame 8; and the inner frame 8 and the intermediate frame 9 are adapted to be displaced in X and Y directions by piezoelectric actuators 11 and 12, in proportion to the voltage applied to piezoelectric actuators. The inner frame 9 and the end frame 10 are coupled through a spring mechanism which is constructed in such a manner as to cross at the central points, and are adapted to be actuated by a piezoelectric actuator 13, thereby effecting minute angular movement about the central point (in the .theta. direction) proportional to the voltage applied to the piezoelectric actuator. A supporting post gripper is fixed to the lower side (not shown) of the end frame 10. The gripper can grip the supporting post 5 so as to deflect the latter in three directions, i.e., X, Y and .theta. directions. The outer frame 7 is fixed to a stationary member.

FIG. 4 shows the arrangement of the whole portion of the invention. The output from the laser diode 1 is detected by a detector 14 and is sent to a controller 15. The controller 15 computes the amounts of driving of three piezoelectric actuators in accordance with the following method, and applies to each piezoelectric actuator a voltage corresponding to the computed value.

A description will be made hereinunder as to the control sequence in the first embodiment of the invention.

It is assumed here that the position of the gripper when it has just gripped the supporting post 5 is expressed by x.sub.0, y.sub.0 and .theta..sub.0, while the output of the laser diode in this state is represented by f.sub.0. When the factors x, y and .theta. have initial values x.sub.0, y.sub.0 and .theta..sub.0, the amounts of initial displacement .DELTA.x.sub.1, .DELTA.y.sub.1 and .DELTA..theta..sub.1 are determined. Symbols .DELTA.x, .DELTA.y and .DELTA..theta. represent the displacements in x, y and .theta. directions, while suffix n represents the n-th cycles of movement.

The optical output f detected by the detector 14 through the fiber is determined by x, y and .theta..

As the first step, a movement by amount .DELTA.x.sub.1 is caused and the gradient of the optical power distribution surface is determined by the difference in the optical output between the state before the movement and the state after the movement. ##EQU1## where, f.sub.0 and f.sub.x1 represent the value of the optical output in the states before and after the movement by the amount .DELTA.x.sub.1.

Then, a movement by the amount .DELTA.y.sub.1 is effected to provide the following condition. ##EQU2## where, f.sub.x1 and f.sub.y1 represent the optical output values obtained in the states before and after the movement by the amount .DELTA.y.sub.1 and can be determined by measurement. Then a movement by the amount .DELTA..theta..sub.1 is conducted so that the following condition is obtained. ##EQU3##

After the completion of movements by amounts x, y and .theta., the gradient s of the optical power distribution surface and the height h are determined as follows. ##EQU4##

Using the conditions of the formulae (1) to (5), the amounts .DELTA.x.sub.2, .DELTA.y.sub.2 and .DELTA..theta..sub.2 of the second cycle of operation in the x, y and .theta. directions are determined as follows. ##EQU5##

A, B, j and k are constants the optimum values of which are obtainable through experiments. If the constant A is positive, the movement is caused in such a direction as to reduce s, whereas, when the constant A is negative, the movement is caused in such a direction as to decrease the value s. It is to be noted also that the amount of movement is decreased as the value h is increased.

Similarly, the amounts .DELTA.x.sub.n, .DELTA.y.sub.n and .DELTA..theta..sub.n in the x, y and .theta. directions in the n-h cycles of movement are determined as follows. ##EQU6##

The cycles of movement are further repeated until the number n exceeds a predetermined value or the value s comes down below a predetermined value or the value h exceeds a predetermined value.

Various methods for determining G(=f(s,h)) employing s and h are usable in place of the formula (9).

FIG. 5 shows the flow of the control method described above. More specifically, FIG. 5a shows the result of application of the control method of the invention to a mechanism having two degrees of freedom in which the output f is given as a function of x and y, i.e., as f=e.sup.- (x.sup.2 +y.sup.2) with the angle .theta. omitted. Numerals appearing in the Figure represents the number of cycles. It will be seen that the output f takes the maximum value of 1 on condition of x=0 and y=0. In this embodiment, conditions of A=0.5, m=0, x.sub.0 =y.sub.0 =1, .DELTA.x.sub.1 =0.1 and .DELTA.y.sub.1 =-0.1 are met. As will be clearly seen from these conditions, the gripper has been brought to the position where the output f takes the maximum value. The output value obtained in this state is shown in FIG. 5b.

In the described embodiment, the movement in respective steps for the purpose of the probing is intended not only for the approach to the designated maximum value but also for the measurement of the gradient in the vicinity of the maximum value point. As a result, an efficient probing is executed because the probing and the measurement of gradient are conducted at one time.

In the severest method, the movement by the amount .DELTA..sub.x in the x-axis direction is followed by the movement in the -.DELTA..sub.x direction, and a subsequent movement .DELTA..sub.y in the y-axis direction is followed by a movement -.DELTA..sub.y, and finally a movement is effected in the steepest direction on the x, y plane. The method of the invention is superior to the above-explained severest method in that (1) the number of the moving cycles is smaller, and that (2) number of sharp turns (movement -.DELTA..sub.x following the movement .DELTA..sub.x means 180.degree. change in the moving direction) is smaller.

A description will be made hereinunder as to the case where the control sequence explained above is applied to displacement of n-th order (x.sub.1, . . . , x.sub.n), with specific reference to FIG. 6.

The distances (.DELTA.x.sub.10, .DELTA.x.sub.20, . . . , .DELTA.x.sub.n0) for the first cycle of movement are beforehand determined, as well as the level of the optical output (f.sub.c) at which the probing is completed and the number Nc of the cycles at which the probing is to be stopped. In Step 104, a movement .DELTA.x.sub.10 is caused in the direction x.sub.1. The amount of change in the optical output is expressed by .DELTA.f. The gradient of the optical power distribution surface shown by the far field pattern in the direction x.sub.1 is expressed as .DELTA.f/.DELTA.x.sub.10 (Step 106). Then, in Step 108, a movement .DELTA.x.sub.20 is effected in the direction x.sub.2 from the instant point. In a strict sense, it is necessary that a backward driving is effected to return the object to the initial position, i.e, to the position taken before the movement .DELTA.x.sub.10. Such a backward movement, however, is omitted in view of the fact that the movement .DELTA.x.sub.10 is negligibly small and in order to shorten the probing time. The inclination during this movement is expressed by .DELTA.f/.DELTA.x.sub.20 (Step 110). Thereafter, the movements .DELTA.x.sub.30, .DELTA.x.sub.40, . . . , .DELTA.x.sub.no are consecutively conducted (Step 112) and inclinations are computed (Step 114). Thereafter, a movement .DELTA.x.sub.1 is effected in the direction x.sub.1. The .DELTA.x.sub.1 is determined in accordance with the formula .DELTA.x.sub.1 =G.sigma.f/.sigma.x.sub.1. The value of inclination calculated immediately after the previous movement in the direction x.sub.1 (.DELTA.f/.DELTA.x.sub.1, .DELTA.f/.DELTA.x.sub.10 for the first movement) is used as .DELTA.f/.DELTA.x.sub.10. The amount of change in the optical output in this state is expressed by .DELTA.f and the inclination during this movement is given as .DELTA.f/.DELTA.x.sub.1 (Step 118). Then, a movement .DELTA.x.sub.2 is effected in the direction x.sub.2, followed by consecutive movements .DELTA.x.sub.3, .DELTA.x.sub.4, . . . , .DELTA.x.sub.n, with calculation of the inclinations 120-128. The probing is continued in the manner described and is ceased when a predetermined value f.sub.c is reached or when a predetermined number of probing cycles is reached.

A second embodiment of the invention will be described hereinunder.

The principle of the second embodiment is as follows. The displacements x.sub.1, x.sub.2, . . . , x.sub.n of n-th order is given as follows.

In this case, the estimation function f is expressed as follows.

Since the value of f (S) is obtained as the optical output at every moment, it is not necessary to provide a practical form of f(S).

The value of the estimation function as obtained when the condition of S=Sm is met is expressed as fm=f(Sm). The gradient e.sub.m of the estimation function is given by the following formula. ##EQU7## where, x.sub.1, x.sub.2, . . . , x.sub.n are unit vectors of each moving direction of the fine motion mechanism. When the amounts of movement are small, these amounts are expressed as .DELTA.x.sub.1, .DELTA.x.sub.2, . . . , .DELTA.x.sub.n. In this case, the gradient e.sub.m is given by the following formula. ##EQU8## where, .DELTA.f.sub.m is the amount of change in the value of the estimation function, which is given by the following formula (20).

As will be seen from formula (20), the gradient e.sub.m varies largely depending on the value of the estimation function, such that it takes a large value in the region where the estimation function has a large value and a small value in the region where the estimation function takes a small value. Thus, the gradient e.sub.m is largely varied by the absolute value. In order to avoid this problem, the amount of change in the value of the estimation function is normalized as follows by the value f.sub.m-1 of the estimation function as obtained before the movement. ##EQU9##

Using the value of gradient e.sub.m * of the estimation function thus obtained, the amount .delta.x.sub.1, .delta.x.sub.2, . . . , .delta.x.sub.n of movement effected by the fine motion mechanism are determined in such a manner as to make the estimation function approach the maximum value from the instant position, i.e., in the direction of e.sub.m *. ##EQU10## wherein A and p are constants (A>0, p.gtoreq.0).

The fine motion mechanism progressively moves towards the direction of the gradient so that the estimation function value reaches the maximum value. The gradient becomes zero when the maximum value is reached. In this state, the mechanism does not work any more, so that the aligning operation is finished.

In this embodiment, the amount of movement to be achieved by the fine motion mechanism is determined on the basis of the gradient which in turn is obtained by normalizing the amount of change in the evaluation function. According to this arrangement, the mechanism is driven in accordance with the rate of change of the estimation function value rather than the absolute value of the estimation function. In consequence, the large amount of movement given by the fine motion mechanism is large when the mechanism is remote from the position corresponding to the maximum value but is small when the position corresponding to the maximum value has been approached, whereby an efficient probing is obtained.

A practical process in accordance with the second embodiment will be explained with reference to FIG. 7.

The displacements of the mechanism when it has just gripped the supporting post 5 by the gripper are given by X.sub.0, Y.sub.0 and .theta..sub.0, while the optical output in this state is represented by f.sub.0. In the first cycle, the X-direction actuator is driven (Step 202) in the X direction by an amount corresponding to the amount .DELTA.X.sub.1 which is set beforehand, and the optical output in this state is measured to obtain the following condition (Step 204). ##EQU11##

Thereafter, operations for driving by previously set amounts .DELTA.Y.sub.1 and .DELTA..theta..sub.1 are conducted both in Y and .theta. directions, so that the following conditions are derived from respective optical outputs f.sub.1Y and f.sub.10.theta. (Steps 206-212). ##EQU12##

Then, the following operations are conducted (Steps 214-244) on the basis of the data shown in formulae (24) to (26).

In the steps 216, 224 and 232, the following averaging operation is carried out to minimize the noise content in the value of the estimation function. ##EQU13##

In formula (27) e.sub.m *1, . . . , e.sub.m-l * represent, respectively, the gradients in the cycles which are 1 to l th preceding cycles as counted from the instant position, and are given by the formula (21). Symbols .alpha..sub.0 to .alpha..sub.l represent the weight coefficients.

The gradient em*X of the optical output fmX in the 3m+1 th cycle (m=1, 2, . . . ) are determined (Step 216) as follows in accordance with the formulae (21) and (27). ##EQU14## Referring to formula (28), the terms .DELTA.fm*X, .DELTA.fm*Y and .DELTA.fm*.theta. in the right side of this formula should be replaced, in a strict sense, with the values which are obtained by normalizing the amount of change in the optical outputs obtained when the fine motion mechanism is driven simultaneously in all directions X, Y and .theta. by amounts .DELTA.X.sub.m, .DELTA.Y.sub.m and .DELTA..theta..sub.m. Practically, however, the normalized values can be regarded as being materially the same as the values .DELTA.fm*X .DELTA.fm*Y and .DELTA.fm*.theta., so that formula (28) is valid.

Referring now to Formula (29), if the condition of m is met, the following condition is established.

and substitute therefor--Regarding formula (29), during the initial stages of the probing control operation wherein a condition 1.ltoreq.m.ltoreq.l is met, the values of the gradient in the preceding cycles which are necessary for calculating Em*X in accordance with formula (29) are those in only 1 to m-th cycles. In the initial stages wherein the condition 1.ltoreq.m.ltoreq.l is met, the following condition is established for calculating Em*X in accordance with formula (29):

The amount .delta.Xm in the X direction is determined in accordance with formula (20) on the basis of the formula (23). ##EQU15##

The values of coefficients .alpha..sub.0 to .alpha..sub.l, l, A and p appearing in formulae (29) and (32) are optimally determined through experiments.

Subsequently, the fine motion mechanism is moved in the X direction by amount .delta.Xm (Step 220) and the (3m+2) th optical output fmY is measured. The gradient Em*Y also is determined (Step 224) as follows. ##EQU16##

Similarly, the amount .delta.Ym of movement in the Y direction is determined (Step 226) by the following formulae. ##EQU17##

Then, the fine motion mechanism is actuated (Step 228) by amount .delta.Y.sub.m in the Y direction and the optical output fm.theta. for (3m+3) th cycle is measured.

The gradient Em*.theta. and the amount .delta..theta.m of movement in the .theta. direction are determined in accordance with the following formulae. ##EQU18##

Then, .DELTA..theta..sub.m+1 is set as .delta..theta..sub.m and 1 is added to m so that the process returns to the initial state and then repeated.

This repetitional operation is continued and is stopped when the optical output f has been increased to exceed a predetermined value F (Steps 222, 230, 238), or when the gradient is decreased to reduce the value .sqroot.Em*.Em* down below a predetermined value E (Step 242) or when the number m of the probing cycles has been increased to exceed a predetermined number M (Step 204), whereby the optical axis alignment is accomplished.

As has been described, in the embodiment of the invention, not only the movement towards the maximum value but also the determination of the gradient of the estimation function value is conducted in each step during the probing, so that it becomes unnecessary to determine the gradients in all directions, thus providing advantages such as higher efficiency of probing, shortening of the probing time, and reduction in the load on the mechanism.

In addition, since the gradient is determined through normalization of the estimation function, the gradient of the estimation function is estimated without being affected by the absolute value of the estimation function, the requirement for a change in the parameter can be reduced even for devices which involve fluctuation of the output.

In addition, since the gradient is determined taking into account also the gradients in the past, it is possible to absorb any abrupt apparent change in the gradient due to noise, so that the probing can be conducted smoothly even though the control is conducted in accordance with differentiated values.