High-resolution optical angle sensors: approaching the diffraction limit to the sensitivity Augusto Garcı´a-Valenzuela, Gabriel E. Sandoval-Romero, and Celia Sa ´ nchez-Pe ´ rez We carry out a detailed analysis of angle-sensitive devices based on the critical-angle effect. We consider their use in measuring small angular deflections of a laser beam. We establish the diffraction limit to the sensitivity for optical-angle sensors based on reflection and transmission of a laser beam. We find that this limit is identical to that of the triangulation scheme when using a position-sensitive detector or the autocollimation scheme. We analyze the main proposals to date of optical-angle sensors based on the critical-angle effect, focusing on their maximum sensitivity and their polarization dependence in practical conditions. We propose and analyze theoretically a novel and simple angle-sensitive device for sensing optical-beam deflections with very low polarization dependence and a maximum sensitivity close to the diffraction limit when used with typical laser beams. We discuss the basic principles for designing this type of device, provide numerical results, and point out a convenient fabrication procedure. © 2004 Optical Society of America OCIS codes: 230.2090, 230.0250, 120.4640, 300.6430, 120.7280, 230.5480. 1. Introduction Optical-beam deflection sensing OBDS is used in many important measuring techniques. Among the most important techniques are cantilever-based sensing, 1–7 photothermal techniques based on mirage detection and reflectance techniques, 8 –14 and optical profilometry. 15,16 Also we can find in the literature examples of high-sensitivity torsion balances, 17 air- borne ultrasonic wave detection, 18 and lamb wave detection. 19 One of the main advantages of OBDS compared with other optical techniques is that it is simple while it offers in many cases the same sensi- tivity as more sophisticated techniques. In all the applications mentioned above the OBDS scheme is implemented with a laser beam. Al- though one may think of a few advantages if it were possible to implement an OBDS scheme with a non- laser optical beam, in practice it has not been possible to come up with a nonlaser optical beam with a de- gree of collimation and optical power comparable with that of a laser beam. Most often, deflection of an optical beam is sensed by using a position-sensitive detector PSD in a tri- angulation scheme see, for example, Refs. 1–15, 20. The most common PSD for sensing optical-beam de- flections in one plane is the split detector SD, also referred to as the bicell detector. The SD consists of two adjacent photodetectors with a thin gap between. To sense small deflections of a laser beam by trian- gulation, one places the SD a distance l away from the deflection point and alienates the detector so that the laser spot is centered on the gap of the SD. If the laser beam deflects by  p , the laser spot at the SD moves sideways by x = l p . The output signal S is taken as the difference between the two photocur- rents i 1 and i 2  divided by their sum: S =i 1 - i 2 i 1 + i 2 . As the beam spot moves sideways to the gap, one of the photocurrents increases, the other decreases, and the output signal changes from zero. One may infer that the larger the distance l, the larger is the sensitivity to beam deflections. How- ever, it is not difficult to show that the sensitivity to lateral displacement of the laser spot S x is pro- portional to the inverse of the spot radius at the detector:  d . 2 Specifically, for a Gaussian beam we have S x = 22 12  d . On the other hand, af- ter some distance, l  l R , the radius of the laser spot starts to increase because of diffraction proportional to l. Then for l  l R the sensitivity to laser deflec- tions remains constant at its maximum possible value. For a Gaussian beam of waist radius  0 we have l R   0 2 , and its value is typically of the The authors are with Centro de Ciencias Aplicadas y Desarrollo Tecnolo ´ gico, Universidad Nacional Auto ´ noma de Me ´ xico, Apartado Postal 70-186, Me ´xico D.F. 04510, Me ´xico e-mail for Garcia- Valenzuela, garciaa@aleph.cinstrum.unam.mx. Received 28 January 2004; revised manuscript received 28 Jan- uary 2004; accepted 3 May 2004. 0003-693504224311-11$15.000 © 2004 Optical Society of America 1 August 2004  Vol. 43, No. 22  APPLIED OPTICS 4311