Basic Principles and Methodologies - Optical Sensors and Their Applications

Optical Sensors and Their Applications

4.3 Basic Principles and Methodologies

will increase in the future. The coherent length of an LD (<1 m) is inherently shorter than that of He–Ne lasers (>1 m), which has been a light source for long-distance measurements based on interferometry.

Therefore, LD is still suitable for short-distance sensors.

On the other hand, the sensing system must be made small enough for the sensors to be installed in mechanical systems. Integration of the optical sensors is also an important consideration in developing the built-in sensing systems. In sensors integrated for pressure and acceleration, the mass-production and assembly of the sensors have been achieved by silicon micromachining. With micromachining technology, the mechanical parts of the sensors are fabricated by semiconductor lithographic processes in a similar way to integrated circuits. The miniaturization of sensors and their integration with electronics are also important for the development of sensors for mechatronics. The microsystems fabricated by silicon micromachining are called microelectromechanical systems (MEMS), whose use has been widely expanded to a broad range of fields, from mechanical engineering to electronics, chemistry, bioengineer-ing, etc. The technology is also merging with optics, which is categorized as optical MEMS. Several optical sensors and optical components have been proposed in which optical detectors, optical components, and mechanical structures are fabricated simultaneously by lithographic processes without the individual components being assembled. Those technologies will become important in the future evolution of integrated sensors.

4.3 Basic Principles and Methodologies

Straightness of light-beam propagation is a simple and useful property of light for alignment and precise displacement measurement. Figure 4.1 shows the schematic diagram of the position measurement using a laser beam and quadrant-cell position sensor. Four photodiodes are installed adjacently and the devi-ations of the laser spot from the center of the quadrant-cell along the x and y axes (UX,UY) are obtained from the photocurrents (I1, I2, I3, and I4) of the cells according to the equations:

(4.1) The linearity of the displacement measurement is limited to a region smaller than the beam spot size.

The alignment between the laser axis and the center of the position sensor is carried out. The displacement signals become zero when the two centers are aligned. The aiming stability of the laser source is as good as 1 µ radian. The measurement sensitivity is also limited by the fluctuation of the atmospheric index due to temperature and airflow. Under the environmental conditions of a quiet laboratory, the displacement sensitivity is around 1 µm, or less, for the alignment of a 1-m-long light beam.

In addition to the measurement of displacement vertical to the optical beam axis, the displacement along the optical axis can also be performed by using the quadrant-cell position sensor. In an optical

FIGURE 4.1 Schematic diagram of the position measurement using a laser beam and quadrant-cell position sensor.

U I I I I

1162_Frame_C04 Page 3 Friday, August 30, 2002 7:18 PM

4-4 Opto-Mechatronic Systems Handbook: Techniques and Applications

disk system, the laser light should be focused on the surface of the rotating disk during operation. The deviation of the focal position from the disk is detected by an optical system shown in Figure 4.2. The reflected laser beam is focused through a convex lens and a cylindrical lens. Because of the cylindrical lens, the focal length in the plane where the cylindrical lens works is shorter than that in the other plane.

Therefore, the laser spot on the quadrant-cell position sensor is circular only at the position where the laser beam is just focused on the disk surface. Otherwise, the laser spot on the position sensor is an ellipse. Therefore, the deviation from the focal position can be detected based on the difference between the two sets of the signals obtained from the two photodiodes located diagonally to one another.

Triangulation is also a simple conventional technique for measuring distance. The absolute value of the distance can be obtained after calibration. The schematic diagram of the triangulation is shown in Figure 4.3. The light emitted from the light source impinges on the object surface. We assume here that the surface is optically rough. The light reflected from the surface is scattered widely around the reflection angle. (If the surface is optically flat, the reflection angle is equal to the incident angle, and the reflected light is not always received by the photodetector.) The reflected light converges on the position sensor through a convex lens. The light spot on the object surface is imaged on the sensor plane by the lens.

The object position is determined from the spot on the sensor. Figure 4.4 shows the principle of trian-gulation. Knowing the length of the base line L and the values of the two angles α and β, the distance h from the base line is obtained from the equation

(4.2) Based on the output of the position sensor, the direction in which the beam is reflected is measured.

The triangulation is widely used in the autofocus of compact cameras. One example of the optical system FIGURE 4.2 Focal position sensing in optical disk system.

FIGURE 4.3 Schematic diagram of sensors using triangulation.

h L

= +

tan tan tan tan

α β

1162_Frame_C04 Page 4 Friday, August 30, 2002 7:18 PM

Optical Sensors and Their Applications 4-5

is shown in Figure 4.5. An infrared light source is used and the reflected light is detected through an aperture or lens. The aperture works to determine the direction of the reflected light by combining the position sensor as shown in Figure 4.5.

In the case of digital cameras and videocassette recorders, a convenient technique for autofocus is image processing. The high-frequency component of the image is extracted from the image detected by the CCD. Under good focus conditions, the high-frequency component of the image is maximized, and the lens position is adjusted to obtain the maximum image size.

The Moiré technique is traditionally used for precise displacement measurements. Figure 4.6 shows the Moiré fringe generated by superimposing two gratings. The period of the Moiré fringe is much larger than that of the gratings. When the angle between the grating lines is increased, the period of the Moiré fringe decreases. Translating a grating in a direction perpendicular to the grating lines, the Moiré fringe FIGURE 4.4 Principle of triangulation.

FIGURE 4.5 Triangulation used in compact camera.

FIGURE 4.6 Moiré fringe generated by superimposed gratings.

1162_Frame_C04 Page 5 Friday, August 30, 2002 7:18 PM

4-6 Opto-Mechatronic Systems Handbook: Techniques and Applications

moves in the direction parallel to the grating lines with a magnified displacement. When the two gratings are parallel, the magnification of the displacement is maximized.

Optical encoders are common displacement sensors that utilize the Moiré effect. Figure 4.7 shows the optical configuration of a conventional optical encoder. The light from the LED is collimated through a convex lens and passes through the scale grating and index grating. The transmitted light is detected by a photodiode placed behind the index grating. The signals from the photodiodes vary nearly sinusoidally with increasing displacement. The index grating usually consists of four phase-shifted gratings for obtain-ing the phase-shifted sinusoidal signals. Those signals are used for the interpolation of the sinusoidal curve and the detection of the direction of motion.

When the period (p) of the grating used in the conventional encoder is decreased, the diffraction effect from the scale grating becomes significant. The gap (z) between the scale grating and the index grating has to be small (z<p²/λ, where λ is the wavelength) for keeping the signal contrast high. The diffraction effect is advantageously used for a novel encoder. Figure 4.8 shows the optical encoder using the diffraction effect of the grating and the interference of the diffracted beams. Fine grating generates the diffraction beams when irradiated by a laser beam. The phases of the diffracted beams are shifted by the translation of the grating. The value of the phase shift θ is given by

(4.3) where d and N represent displacement of the grating and the order of the diffraction beam. In Figure 4.8, the ±first-order diffraction beams interfere to obtain the sinusoidal signal as a function of the displace-ment. The total phase difference between the interfering beams is twice as long as the value of Equation 4.3; thus, the period of the displacement signal is half the period of the grating.

There is another way to avoid the decrease of the signal contrast when the gap between the gratings is wide. Grating-image-type encoders are based on a different principle [Hane et al., 2002], although the FIGURE 4.7 Optical configuration of a conventional

optical encoder.

FIGURE 4.8 Interferometric encoder.

θ=2πd pN

1162_Frame_C04 Page 6 Friday, August 30, 2002 7:18 PM

Optical Sensors and Their Applications 4-7

optical configuration is similar to the conventional one. Figure 4.9 shows the schematic diagram of the reflection-type encoder using grating imaging. Unlike the conventional Moiré encoder, object grating is placed in front of the light source. The object grating illuminated incoherently with the light source (here, LED) is imaged through the scale grating onto the index grating by the diffraction effect of the scale grating. Figure 4.10 shows the equivalent optical system of the grating-image-type encoder. The optical system consists of three gratings placed in tandem. Central grating acts as a pupil in the sense that the grating-like image is generated on the plane of the index grating. The superposition of the image and the index grating produces the Moiré fringe. The grating-like image is essentially generated by the diffraction of the central grating. The image is generated under spatially incoherent illumination. Due to the imaging effect, the gap between the gratings is set to be much wider than that used in the conventional Moiré encoder, where the simple shadow of the scale grating is used. To make a high signal contrast obtainable, the combinations of the periods of three gratings are p1:p:p2= 2p:p:2p and p:p:p for the optical configuration shown in Figure 4.10. In the case of the combination p:p:p, the image contrast is not degraded by the polychromaticity of the light source. Therefore, white light can be used for the encoder.

The interferometer is also a valuable instrument for displacement measurement and has been studied for a long time. Figure 4.11 shows the basic optical configuration of the interferometer (Michelson interferometer). The laser beam is divided into two beams by a beam splitter. One beam is reflected by the reference mirror fixed on an optical bench. The other beam is reflected by the mirror fixed on the object for measuring the displacement. Two reflected beams interfere with each other after being com-bined on the photodetector. The interference intensity I is given by the equation,

(4.4) where I1 and I2 are the intensity of the respective beams. The symbol k represents a wave number equal to 2π/λ, where λ is the wavelength. The round-trip optical paths of the two arms in the interferometer are indicated by L1 and L2, respectively. The initial phases of the respective beams are represented by δ1

and δ2. The intensity I varies sinusoidally as a function of the optical path difference L1−L2. Therefore, FIGURE 4.9 Grating-image-type encoder.

FIGURE 4.10 Optical configuration of grating image.

I= + +I1 I2 2 I I1 2cos( (k L L1− 2)+ −δ δ1 2)

1162_Frame_C04 Page 7 Friday, August 30, 2002 7:18 PM

4-8 Opto-Mechatronic Systems Handbook: Techniques and Applications

the displacement d(= ∆L1/2) is measured by λ/2 by feeding I into the up-down counter connected to the photodetector. The phase-shifted displacement signal, which is needed for the interpolation and deter-mination of the direction of motion, may be obtained by tilting the reference mirror to generate a fringe where the phase-shifted signals are spatially generated.

The contrast V of the interference is defined by the equation:

(4.5) where Imax and Imin are the maximum and minimum values of the interference intensity I. The maximum contrast is obtained when the intensities of the two beams are equal to each other and the laser has high temporal coherence.

The heterodyne interferometer is convenient instrument for obtaining high resolution and sensitivity in displacement measurement. Figure 4.12 shows the schematic diagram of the heterodyne interferometer for displacement measurement. Unlike the interferometer shown in Figure 4.11, a two-frequency laser, generally the Zeeman He–Ne laser, is used. Applying a magnetic field causes a Zeeman splitting of the laser level. Two linearly polarized laser beams with a frequency difference of around 2 MHz or 100 kHz are generated depending on the direction of the applied magnetic field. The light beams reflected from the mirrors are interfered with after passing through the polarizer. Under static conditions, the beat of FIGURE 4.11 Optical interferometer used for displacement measurement.

FIGURE 4.12 Heterodyne interferometer for displacement measurement.

V I I

I I

I I I I

= −

+ =

max min

2 _{1 2}

1 2

1162_Frame_C04 Page 8 Friday, August 30, 2002 7:18 PM

Optical Sensors and Their Applications 4-9

the two-frequency lasers is obtained at a difference frequency. The interference intensity is given by the equation,

(4.6) where ∆ω is equal to the difference of the two angular frequencies of the lasers. The wave number k is approximately given by the averaged value for the two laser lights. ∆L is equal to L1 −L2. The initial phase is represented by δ. The phase difference caused by the displacement ∆L or the object velocity ν(∆L= νt, where ν is the object velocity) can be measured easily by an electronic phase meter. Because of progress in the design and manufacture of electronic instruments, the displacement and velocity can be monitored precisely in the heterodyne interferometer. A sensitivity of better than 10 nm is obtained in a commer-cialized heterodyne interferometer. The heterodyne interferometer can also be constructed by using the acoustic optical modulators for generating two frequencies from a single-frequency laser.

Techniques using laser speckles are also novel for sensing the displacement because the motion of an object with a rough surface is detected using simple optics. A speckle is the light intensity distribution generated by the interference of multiple beams reflected from the rough surface. Speckle characteristics such as average diameter and statistical distribution of intensity are not dependent on the surface properties when the surface is rough enough compared with the optical wavelength. Figure 4.13 shows the schematic diagram of the displacement measurement method using the laser speckle. The optical configuration is very simple. The surface is irradiated by a laser beam, and the scattered light that is the speckle field is received by an image sensor such as a CCD. Translating the object, the speckle field shifts at a magnification that depends on the optical configuration. The speckle field changes gradually as displacement increases. When the correlation between the speckle images before and after the movement is calculated, the correlation peak shifts according to the displacement as shown in the inset in Figure 4.13.

The correlation can be calculated by the equation,

(4.7) where Γ is the correlation function, I1(x, y) is the light intensity distribution before the movement, I2(x+

∆x, y +∆y) is that after the movement. S is the area where the integration in the image plane takes places and it includes many speckles. When the object displacement increases, the part of the area in the laser spot leaves the irradiated area and part of the area outside the spot enters the irradiated area. Therefore, the correlation between the areas irradiated by laser light before and after the displacement decreases as displacement increases. Displacement is measured step by step in the region where the correlation is maintained. To calculate the image correlation, an image sensor and computer are needed, but the measurement is carried out with very simple optics.

FIGURE 4.13 Displacement sensor using laser speckle.

I= + +I1 I2 2 I I1 2cos(∆ωt k L+ ∆ +δ)

Γ ∆ ∆( x, y) ( , ) ( ∆ , ∆ ) S I x y I x x y y dxdy

=¹

∫∫

¹ ² + +

1162_Frame_C04 Page 9 Friday, August 30, 2002 7:18 PM

4-10 Opto-Mechatronic Systems Handbook: Techniques and Applications

For some industrial applications the object frequently has a rough surface, which can cause random scattering. A speckle interferometer has been already developed for this requirement. A kind of Moiré fringe is generated between a pair of the speckle patterns obtained before and after the object displace-ment. Statistical image processing, however, is usually necessary to extract the displacedisplace-ment.

Dans le document OPTO-MECHATRONIC SYSTEMS HANDBOOK (Page 119-126)