FIGURE 6.113 A schematic diagram of the basic optical-beam-deflection (OBD) sensing configuration.

A schematic diagram of the basic OBD sensing configuration is illustrated in Figure 6.113. In this case, the displacement, u, of the surface causes the position of the reflected beam on the PSD to move from point P to point P′; the positional change produces a change in the output voltage of the PSD. The output voltage, V, of the PSD electronics can be calibrated in terms of the actual displacement, u, by measuring V versus u for known displacements.

OBD sensing has been used in a variety of applications, including photothermal optical beam deflection (PTOBD) spectroscopy [1], absolute measurement of optical attenuation [2], PTOBD imaging of surface and subsurface structure [3], photothermal displacement spectroscopy [4], atomic-force microscopy [5], and materials characterization [6]. It has also been used as an uncomplicated, sensitive, and accurate method of measurement of surface motion for scanning tunneling microscope scanner transducers [7] and ultrasonic transducer imaging [8].

Theory

The three basic types of devices for OBD sensing are (1) a photodetector behind a sharply edged screen (a knife edge); (2) a small array of photodetectors separated by relatively small, insensitive areas (bicell, quadcell); and (3) a continuous solid-state position sensor (one or two dimensional). Sensing characteristics of a device are determined by the effect of optical beam displacement on the photodetector power distribution. Since laser beams are commonly used in OBD sensing, the analysis involves the assumption that the spatial distribution of the intensity (I) in the plane perpendicular to the direction of wave propagation is axially symmetric with a Gaussian radial variation.

Knife-Edge Photodetector

The essential features of a PSD are represented by a photodetector shadowed by a semi-infinite knife edge, y < 0, as illustrated in Figure 6.114. As can be anticipated from the symmetry of the arrangement and proved mathematically, the maximal deflection sensitivity occurs when the undeflected beam is centered on the knife edge. The intensity of the light reaching the photodetector due to the displacement (u) of the center of the beam is given in the reference frame of the displaced beam by:

© 1999 by CRC Press LLC

FIGURE 6.114 Essential features of a position-sending detector (PSD), as represented by a photodetector shadowed by a semiinfinite knife edge.

where P is the total incident beam power, a = 2/r12, r1 is the Gaussian beam radius, and r ′2 = x′2 + y ′2. In terms of the coordinates (x,y) of the undeflected beam, the rectangular coordinates of the deflected beam are x ′ = x and y ′ = y – u. The power (Pd) on the detector is thus given by:

where erf is the error function. One can see by inspection of Equation 6.127 that the essential characteristics of this position sensor are determined by u/r1. The normalized response, Pd /P, is shown in Figure 6.115 as a function of u/r1. When u = r1 , then Pd = 97.7% P.

The deflection sensitivity is given by the slope of Equation 6.127,

Define the small-signal position sensor sensitivity (units of m–1):

© 1999 by CRC Press LLC

FIGURE 6.115 The normalized response Pd /P as a function of u/r1 (u = displacement of center of beam; r1 = Gaussian beam radius; Pd = power on the detector; P = total incident beam power).

The optical power reaching the photodetector for small signals is then given by:

The photodetector signal will be linear in displacement if u ≤ 0.387r1.

The photocurrent is:

where K is the photodetector responsivity in A/W. The position sensor voltage is obtained using a transimpedance amplifier with gain Z:

Bicell Detector

The deflection of a Gaussian beam initially centered in the insensitive gap of a bicell detector is illustrated in Figure 6.116. The power incident on the upper half of the bicell is given by:

© 1999 by CRC Press LLC

FIGURE 6.116 Deflection of a Gaussian beam initially centered in the insensitive gap of a bicell detector.

The power incident on the lower half of the bicell is given by:

The photocurrent from each detector of the bicell is converted to voltage by identical transimpedance amplifiers: V2 = KZP2 and V1 = KZP1; a difference amplifier is then used to obtain the bicell signal voltage:

The normalized response, 2V/(KZP), is shown in Figure 6.117 as a function of u/r1 for y1 = y2 = r1 /10. Suppose that the beam is centered in the gap, y1 = y2; then, for small displacements, one obtains:

This quantity is optimized when r1 = 2y1, and the optimal sensitivity is 0.484/y1.

© 1999 by CRC Press LLC