Abstract: A multi-beam detecting apparatus adapted to an optical system in which a recording medium is scanned by a plurality of light beams emitted from respective light sources, includes a photodetector, a light interrupting member, and a control circuit. The photodetector produces detection signals when the corresponding light beams come to a predetermined position. The light interrupting member is interposed between the light sources and the light detecting member, and has transparent portions related to the respective light beams. A controlling circuit controls ON/OFF states of the light source in accordance with the respective detection signals related to the corresponding light beams passing through the respective transparent portions in the light interrupting member.

Abstract: A laser beam scanner comprising a laser source, apparatus for producing a scanning beam and a reference beam which are generally parallel, apparatus for directing the scanning beam onto a surface to be scanned, and apparatus for determining the position of the scanning beam in real time in two dimensions by sensing the position of the reference beam, and wherein the apparatus for sensing the position of the reference beam comprises a grating disposed along a scan axis and defining a multiplicity of first grating lines along the scan axis, which permit the definition of the position of the reference beam in a first dimension, a second grating line disposed across the multiplicity of first grating lines and first and second sensors disposed at respective sides of the second grating line, for sensing the relative amount of light impinging above and below the second grating line, for permitting the definition of the reference beam in a second dimension, whereby the position of the reference beam may be determined

Abstract: An optical scanning apparatus for plane surfaces (13) having a laser light source (20), a light deflecting means (16) illuminated by the laser beam, a telecentric image forming element (15) and a light receiving means. Parallel to the scanning line (11) generated by the light deflecting means (16) and the telecentric image forming element (15) there is arranged, at the angle of regular reflection, an image forming retroreflector (12; 38,39) which forms an image of the light bead running along the scanning line (11) on itself.

Abstract: An optical scanning device for mechanically scanning images at a high scan ate over a wide field of view and under low light conditions. The device comprises a first rotating reflecting means such as mirrors for intersecting an input beam of light in a first path and for redirecting the beam of light into a second path. A second rotating reflecting means intersects the second path and reflects the beam of light into a third path, onto a detecting device for detecting the presence of predetermined images in the beam of light. In order to reflect the light beams over an elliptical path the mirrors are mounted on rotating shafts at a slight angle from the perpendicular to the axis of the rotating shaft. The mirrors are rotated at varying speed relationships to each other and varying phase relationships to each other in order to produce a variety of scan patterns.

Abstract: A beam position detector, particularly for use in a scanned laser beam printer, in which the scanned beam is reflected by a mirror to a light sensor. In order to align the mirror, a mirror holder is rotatable on a base plate also holding the sensor. The mirror is also tiltable with respect to the base plate.

Abstract: A light deflector such as a polygon mirror deflects a synchronizing light beam and a scanning light beam which are applied thereto at different angles. A first focusing optical system is disposed between the light deflector and an object to be scanned by the scanning light beam for focusing the scanning light beam on the object. A synchronizing signal generator including a reference grating plate generates a synchronizing signal from the synchronizing light beam applied to the reference grating plate. A second focusing optical system is disposed between the first focusing optical system and the reference grating plate for focusing the synchronizing light beam applied through the first focusing optical system on the reference grating plate. Image information is read from the object or read on the object based on the synchronizing signal.

Abstract: A laser beam scanning apparatus comprises a first mirror provided for reflecting a light path between a deflector and recording medium, a beam detecting sensor for determining a start position for recording by the beam on the recording medium, and a second mirror for guiding the beam reflected by the first mirror to the sensor. The second mirror is arranged such that the beam from the first mirror is guided to the sensor after it is reflected at least one time by said first mirror. In addition, the second mirror is arranged such that on the equation .theta..sub.2 =2.theta..sub.1 is satisfied where .theta..sub.1 and .theta..sub.2 respectively denote the inclination of the first and the second mirrors to a plane orthogonal to a surface of scanning of the beam.

Abstract: In an optical unit for use in a light beam scanning apparatus, a housing that covers optical elements of which the optical system of said apparatus is composed is provided, and the optical elements that need occasional replacement are grouped into blocks as small units which are adapted to be individually remountable in the process of replacement without destroying the hermeticity of the interior of the housing. Being so designed, the optical unit enables the necessary optical elements to be sufficiently dustproof to ensure reliable operation of the light beam scanning apparatus.

Abstract: A laser beam emitted from a laser source is deflected by a light deflector such as a rotational polygonal mirror or a galvanometer mirror to scan a surface-to-be-scanned. A beam position detector detects the incident position of the laser beam on the light deflector, and a control circuit drives an optical path changing mechanism according to the output of the beam position detector to change the optical path of the laser beam upstream of the light deflector so that the laser beam impinges upon the light deflector at the regular position.

Abstract: A scanning optical microscope which comprises a source of optical radiation and means for focussing radiation from the source into an interrogating spot on a surface under examination. The spot is deflected about a point on the surface, and the surface topography is measured by measuring the amplitude and/or phase of the radiation reflected from the surface at the spot position.

Abstract: An image scanning apparatus including a scanning optical system, an image sensor for converting an image beam received from the scanning optical system into an electric signal, and a projecting lens disposed on an optical path between the scanning optical system and the image sensor. The projecting lens is movable along the optical axis for varying projecting magnification. A swing mirror is additionally provided on the optical path between the scanning optical system and the projecting lens. When in an operative position, the swing mirror intercepts the optical path and establishes a shorter optical path for use in obtaining the image of a film or the like in super-magnification.

Abstract: This invention relates to a pyramid polygon scanner without cylinder optics wherein the effects of jitter are reduced by the use of a start of scan detector situated at a predetermined angle from the normal (vertical) position. The start of scan detector is rotated about an axis through the nominal scan line. Thus, if tilt (not the draft angle) is present in the rotating polygon system and jitter is generated, the rotation angle of the split detector moves the jitter to the beginning and end of scan, leaving the center of scan free of the effects of jitter. The angle of the split detector is in approximate relation to the angle of incidence at the first reflection on the rotating polygon.

Abstract: A novel apparatus for use in generating a scan timing signal in a laser raster scanner includes an optical diffuser positioned to receive a scanned reference beam through a reference mask. The diffused, modulated reference beam is presented to an array of photodetectors. The number of photodetectors in the array is selected to be sufficient so that at least two photodetectors receive the diffused modulated reference beam simultaneously as the reference beam is scanned along the reference mask.

Abstract: A beam splitter (120) arranged in the radiation path of the scanning beam splits off a reference beam synchronously moving with the scanning spot (21) to a reference plane (140). The movement of the scanning spot (21) can be checked by measuring, with the aid of a radiation detector (160), the movement of a reference spot (121) formed by the reference beam in the reference plane. In this way an accurate determination of the position of the scanning spot (21) is possible while using simple beam-deflecting elements (40,42) having a relatively low accuracy. A cylindrical lens (131) gives the scanning spot the shape of a line, so that sensitivity to dust and other contaminations on the reference plane is reduced considerably.

Abstract: An optical system, useful for a flying-spot scanning apparatus includes a laser tube, an acousto-optical modulator, a deflecting mirror directing the laser beam in a first direction, and an objective lens having the characteristic of h=f.multidot.sin .theta., where h is the distance on an object between the optical axis and the point upon which the laser beam impinges, f is the focal length of the objective lens and .theta. is the angle formed by the beam entering the objective lens with respect to the optical axis. The objective lens includes a first optical unit having the negative focal length and a second optical unit having a positive focal length. The third-order distortion coefficient of the objective lens is approximately "1". Straight and parallel scanning loci can be effected on a recording medium, as the recording medium is fed in a second direction.

Abstract: A light beam scanning device includes a reference grid plate, a resonant light deflector for deflecting a light beam to cause the light beam to scan the reference grid plate through an f.theta. lens for thereby enabling the reference grid plate to produce a pulse signal, and a PLL circuit for generating a synchronizing signal from the pulse signal to read or record image information. The reference grid plate has slits defined at intervals, the slit intervals in that area of the reference grid plate which produces a pulse signal that is not directly contributed to the recording or reading of the image information being progressively smaller toward an end of the reference grid plate according to the scanning speed of the light beam.

Abstract: In a scanner for the optical checking of objects such as CD-discs there is provided a coherent light source; a light deflecting device which allows a light beam emitted from the light source to sweep over the object in a substantially linear scanning movement, with the optical axis of the light beam subtending a small angle with a normal to the object surface transverse to the scanning direction; and a detector for detecting light which is reflected back from the object. In the present arrangement the optical axis of the light beam also subtends a small angle with the normal to the object surface in the scanning direction. This makes it possible to avoid disturbing modulation of the detector signal due to interference effects.

Abstract: Apparatus for monitoring the eye of a subject comprising: apparatus for directing infra-red radiation at the eyes of a subject; apparatus for sensing infra-red radiation retroreflected by the retina through the cornea of the subject; and apparatus for providing a sensible output indication in the absence of expected received retroreflected radiation, indicating the closing of the subject's eyes or direction of his eyes outside of a desired angular region.

Abstract: An optical beam scanner includes a light source, a deviation unit for deviating a beam from the light source and emitting a scanning beam, a compensation unit for compensating a vertical inclination of the deviation unit and having a first optical element for deforming the scanning beam into a vertically longitudinal oval shape and a second optical element for reforming the oval beam into a round shape and converging the scanning beam on a scanning surface. A detection unit detects the scanning beam and is disposed between the deviation unit and the second optical element.

Abstract: A synchronizing device is used in a laser printer which comprises a polygonal mirror for periodically deflecting a laser beam which scans a scanning plane and a photodetector provided on the scanning plane outside a region in which a printing is made by the laser beam for outputting an output signal when the laser beam is detected. The output signal of the photodetector is used for producing an image scan clock signal which synchronizes each scan of the laser beam.

Abstract: A synchronizing signal generating system for a laser scanner comprises a source for emitting a first laser beam for scanning and a second laser beam for synchronization of scans by the first laser beam, a polygonal mirror for causing the first laser beam to scan a medium and for causing the second laser beam to scan a grating which has bright portions and dark portions alternately arranged along a scanning direction of the second laser beam, a converging optical system for converging the second laser beam transmitted through the grating, a light receiving system for receiving the second laser beam converged by the converting optical system and for generating a synchronizing signal, and a circuit for controlling the source responsive to the synchronizing signal so as to synchronize a scan timing of the first laser beam. The converging optical system comprises a plurality of lenses or concave mirrors provided for a length corresponding to a scan length of the second laser beam on the grating.

Abstract: A variable phase time delay and signal aggregation ssystem is disclosed. The invention is adapted for use in scanning detection system and serves to maintain spatial resolution on a target surface independent of scan angle. The invention includes means for detecting electromagnetic signals from the surface area. The detector means includes a plurality of detector elements. Each detector element generates a corresponding first plurality of output signals representative of the response of the detector to energy received from the surface area within the field of view of the detector as the detection system scans through a predetermined range. Control means are included for selectively clocking the output signals from the detector elements to phase the relative timing thereof as a function of the scan angle. Means are included to aggregate these signals to generate a combined output signal having the predetermined spatial resolution.

Abstract: There is disclosed an optical measuring apparatus including a light scanning section for converting a light beam from a first light source to a parallel scanning light beam, a focussing section including a first focussing lens for focussing the parallel scanning light beam, an electric signal generating section for converting a focussed light to an electric signal, a measuring reference signal generating section and an electric signal processing section.The light scanning light section comprises a first mirror and a second mirror, each of which is rotated synchronously. The measuring reference comprises a transparent scale which is rotated in synchronism with the first and second mirrors, a light source, a second focussing lens and a second photoelectric conversion element. The electric signal processing section processes the electric signal from the electric signal generating section based on the measuring reference signal.

Abstract: A shift mirror or reflector (SP) which is noted by high azimuth velocity around a first axis (A1) and dependent upon that can be tilted around an axis rotating therewith. The rotary movement is transmitted from a motor (M) arranged at the side by means of a belt drive (RS) (Z1) or directly from a coaxial hollow shaft motor (M1) via a first shaft and a reflector-suspension to the reflector. The tilt movement arises from an up and down movement of a second shaft via tilt levers (K1, K2), with the second shaft being guided within the first shaft and rotating therewith. The second shaft (A2) is coupled via an axial bearing to the up and down movement of a spindle/nut arrangement, which is actuated by a separate drive (RS2) or another hollow shaft motor (M2). First shaft, second shaft, spindle, nut and also, if desired, the hollow shaft motors are arranged coaxial to each other.

Abstract: A light guide of an elongate shape having rectangular cross section, e.g., a quandrangular prism, directs, toward a light detector, either light emitted by applying a scanning light beam to an object and indicative of image information or a synchronizing light beam divided from the scanning light beam. The light guide has at least one outwardly spread end at which the light detector is disposed. The emitted light or the synchronizing light beam which has entered the light guide is totally reflected in the light guide by an inclined surface thereof progressively inclined in a direction toward the spread end, so as to be directed toward the light detector.

Abstract: In a deflection scanning optical system, a single first mirror is arranged between a laser beam source and a surface to be scanned. The first mirror has a first reflecting section, a second reflecting section and a transparent section. The laser beam from the laser beam source is reflected by the first reflecting section. A second mirror is provided for reflecting the laser beam reflected by the first reflecting section, toward the second reflecting section. The second mirror also reflects the laser beam reflected by the first reflecting section to transmit the reflected laser beam through the transparent section, thereby directing the transmitted laser beam toward the surface to be scanned. A detector received the laser beam reflected by the second mirror toward the second reflecting section and reflected by the same, for detecting a scanning position of the laser beam with respect to the surface to be scanned.

Abstract: In a film image reading out device, in which one surface of a film, where images are recorded, is scanned repeatedly with a laser light beam along a scanning line and images are read out by detecting continuously light, which has passed through the film, while moving the film with a low speed in the direction, which is perpendicular to the scanning line, a light diffusing member is disposed closely to the surface opposite to that of the film scanned with the laser light beam and the optical density of the film is detected continuously by leading transmitted and diffused light to a photodetector by means of a bundle of optical fibers.

Abstract: A laser scanning apparatus is characterized by a curved film-receiving field with a conforming photodetector assembly. In one embodiment, the photodetector assembly comprises a plurality of semiconductor elements. In other embodiments, the photodetector assembly includes a photodetector device mounted in light transmissive engagement with a transparent block for receiving light passed through a radiographic film.

Abstract: A method and apparatus for recording the image of an object, for instance the earth's surface, from a flying body, in this case an earth satellite. The flying body flies over the object at an altitude. Herein, the object is scanned in lines by a line scanner. The viewing angle .alpha. of the liner scanner with respect to the direction of flight v is increased during the scanning process, whereby a higher resolution capacity is attained. Preferably several line sensors are used in the line scanner, which are arranged on a carrier, which is displaced during the flight of the flying body relative to a length in the direction of flight v. The displacement occurs by way of a cyclically functioning drive.

Abstract: A scanning light beam is reflectively deflected by a light deflector in a main scanning direction substantially perpendicular to a subscanning direction in which an object surface to be scanned is moved. The deflected scanning light beam is passed through a scanning lens to scan the object surface in the main scanning direction. A synchronizing light beam is applied to the light deflector at a position where the scanning light beam is reflected thereby, in a direction allowing the synchronizing light beam that is reflectively deflected by the light deflector to be applied to the scanning lens. A converging lens is disposed on the optical path of the synchronizing light beam prior to application to the light deflector. The synchronizing light beam having left the scanning lens is passed through a grid and detected by a light detector assembly.

Abstract: A galvanometric optical scanning system is disclosed. In order to compensate errors in phase, zero drift etc., at least two synchronization photodetector means are provided in an optical path of scanning beam of light. The pulses produced by the photodetector means are processed to generate correction signals for various commpensations.

Abstract: A galvanometric optical scanning system is disclosed. In order to compensate errors in phase, zero drift etc., beam position detection means is provided in an optical path of scanning beam of light and comprises a pair of closely located photodetectors. The pulses produced by the beam position detection means are processed to generate correction signals for various compensations.

Abstract: An inspection apparatus for inspecting, for example, sheet material, in which a beam of radiation 12 is scanned across a sheet 13 by means of a first facet 41 of a rotating mirror drum 22. Scattered radiation from the sheet is received by a second facet 46 and 2 is passed to a photodetector 49 for analysis.

Abstract: An optical scanning system (10) is disclosed for scanning a wide incoming field of view of at least 60 degrees. The system (10) incorporates two flat mirrors (12,26) which rotate about two axes (20,28). The motion of the two mirrors is synchronized. The resulting scanned image is directed onto a sensor (54) with minimal rotation and distortion of the image.

Abstract: A light beam scanning read-out apparatus and a light beam scanning recording apparatus comprise an optical system for converting light guided inside of an optical waveguide into collimated optical wave, a device for generating surface acoustic waves which deflect the guided optical wave, a drive circuit for operating the surface acoustic wave generating device so that the frequency of the surface acoustic waves changes continuously, and a focusing grating coupler for converging the guided and deflected optical wave at a space outside of the optical waveguide. The read-out apparatus further comprises a sub-scanning device for moving a read-out original exposed to the converted light with respect to the optical waveguide, and a photodetector for detecting light obtained from the read-out original.

Abstract: The position and motion of a rotating element is determined by using a two-grating moire pattern. Movement of the element causes a projected scale image representing radiation reflected from the element to shift relative to a fixed grating thereby generating moire fringes. The accumulated fringes serve to measure absolute position and motion of the element.

Abstract: The speed at which a desired surface is scanned by a light beam is rendered constant by correcting the frequency of an image scanning clock signal without using an f lens. The characteristics of correcting the image scanning clock frequency can be varied, or the image scanning clock signal can be brought into phase with a recording position signal.

Abstract: In a method and an arrangement for aligning, examining and/or measuring two-dimensional objects situated on a table of a measuring machine, which table is displaceable at least in two coordinate directions extending perpendicular to one another, light fluxes which are distinguishable according to the associated coordinate direction and which are combined in a beam path and which are imaged in a common intermediate image plane and which are deflected by an optical element according to the coordinate directions associated with them are projected by an imaging system onto the object to be measured in each instance. For the illumination of the respective object structures, an illuminating beam is generated for each coordinate direction, and the object structures illuminated by means of this beam are imaged, separately according to coordinate directions, on scanning means.

Abstract: A modulated laser beam emitted from a semiconductor laser is deflected by a rotating light beam deflector to scan a desired surface. The frequency of an image scanning clock signal and the intensity of the laser beam from the semiconductor laser are varied according to a scanning rate at which the surface is scanned by the modulated laser beam.

Abstract: In the disclosed device, a lens arrangement focuses light upon a detecting sensor arrangement as a vehicle passes over an object, such as the ground, whose surface is to be determined. An optical device slews the path of light to the lens arrangement from left to right relative to the direction of vehicle movement. In one embodiment, a four-part prism rotating on an axis along the direction of vehicle movement passes light through three lenses angled down, for, and aft the vertical and separate radiation detectors simultaneously sense radiation from the earth's surface. In another embodiment, a rotating hexagonal prism has outer reflecting surfaces skewed normal, for, and aft, so that a single lens views sequential signals and applies them to a radiation detector. The signals are sampled, held, digitally converted, recorded, and stored.

Abstract: An optical imaging system is provided with a pulsed laser rangefinder comprising a transmitter 10 aligned with the boresight of the imaging system, the return pulse being focussed by the telescope 6 of the imaging system upon its multi-mirror, two-rotor arrangement 2, 3 and reflected then to a detector 12 and display 13. To eliminate the effect of rotor rotation during the time-of-travel of the pulse, the latter is first reflected from the rotors to a beam reverser 14 including a 90 degree roof-reflector 18 (FIG. 2), which reflects the pulse back to the rotor mirrors in the same vertical plane and then to detector 12 along a path having a fixed spatial relationship to the path to the imaging-system detector 8.

Abstract: A synchronizing light beam detecting apparatus is provided in a light scanning system, such as a laser printer, which includes a light source for emitting a light beam, a polygonal mirror driven to rotate for deflecting the light beam over a predetermined angle repetitively, and a f.theta. lens for focusing the deflected beam along a predetermined imaginary scanning line. The detector includes a cylindrical lens for receiving the light beam passing through the f.theta. lens and picked up at a predetermined position and a detector surface for receiving the light beam passing through the cylindrical lens. A conjugate relation is established between the light beam deflecting point at the polygonal mirror and the detector surface so that the effect of inclination of a mirror surface of the polygonal mirror is cancelled. The detector surface is so located that the light beam is formed thereon only by the image-forming action of the f.theta.

Abstract: Scan distortion is eliminated in a light beam positioner utilizing a first mirror for deflecting a light beam in a first direction in response to a first compensated control signal. A second mirror receives the light deflected from the first mirror and, in response to a second compensated control signal, deflects the received light beam at a second angle in a second direction which is orthogonal to the first direction. An objective lens is provided for focussing the deflected light beam produced by the second mirror. A controller means generates first and second uncompensated control signals which are respectively proportional to the first and second angles of deflection. A scan distortion compensating circuit generates first and second intermediate signals which are respectively dependent on the first and second uncompensated control signals.

Abstract: Apparatus and a method for providing measurements of the diffuse transmittance or reflectance of a sheet at a set of points arranged along a pattern line on the sheet. In accordance with the invention, the sheet, such as a photographic film, is moved with respect to a cylinder with a slot cut in its wall parallel to its central axis. A beam of radiation is swept parallel to the slot and into the cylinder after scanning along a line on the sheet. The inner wall surface of the cylinder is coated with a high reflectance material so that a fraction of the directly transmitted and scattered radiation in the cylinder enters one or more electronic radiation detectors coupled to the cylinder. The fraction of the radiation measured depends on the position along the slot of the radiation beam, and the data are corrected by dividing the measurement at each point by the measured radiation at that point when no object is in the beam. Several embodiments of the cylinder are disclosed.

Abstract: In a light beam scanning apparatus, two photodetectors are positioned in spaced relation by a predetermined distance within a scanning region in a main scanning direction. The start and the end of scanning in the main scanning direction are detected by the photodetectors. The scanning speed of a main scanning means is controlled so that a predetermined number of pulses of a pulse signal having a predetermined period are input within the time between the start and the end of scanning in the main scanning direction. Or, a single photodetector is positioned within the scanning region, and the scanning time from the start of scanning to the photodetector is detected by use of the photodetector. The initial position of scanning is controlled so that a predetermined number of pulses of the pulse signal having a predetermined period are input within the scanning time.

Abstract: An optical projection system, e.g., an imaging infrared system, is compensated for errors caused by scan-to-scan jitter, framing jitter, vibrational effects, and scan nonlinearities. One or two closed control loops compensate for errors associated with mirrors (32, 52) of the optical projection system. In the scan control loop, a set of scan reference marks (75) in a reference plane (7) is superimposed onto a scan position detector (59) lying in a plane (10) containing a detector array (9), producing a scan error compensation signal (56). For wide scan fields of view (72), the scan position detector (59) comprises two pairs (94, 95) of triangular detectors, and means (86) for periodically switching therebetween.

Abstract: A printing apparatus comprising: an elongate platen; a guide member extending parallel to the platen; a carriage slidably movable on the guide member; a printing head mounted on the carriage; an image reading device including an image-reading portion for reading images on a recording medium on the platen, the image-reading portion being movable between a reading position adjacent to the recording medium, and a retracted position spaced from the reading position in a direction away from the recording medium; and a device for engagement of the image reading device with the carriage, to permit the image reading device to move together with the carriage. The image reading device may be supported pivotally by the guide member in the form of a rod. The carriage may have a stopper abutable on the image reading device to determine the reading position of the image-reading portion. The apparatus may further comprise a member for checking optical sensitivity of the image reading device.

Abstract: Integrations of the historical numbers of times that a light beam scanned in an oscillatory course by a self-resonant galvanometer scanner does traverse so far in a first direction so as to impinge upon a Beginning-of-Trace (BOT) sensor, and does traverse so far in the opposite direction so as to impinge upon an End-of-Trace (EOT) sensor, are each used to separately control the voltage level developed in a first, BOT, electrical tank circuit and in a second, EOT, electrical tank circuit. Voltage from each tank circuit is amplified and applied to drive the self-resonant scanner, at a polarity to induce continued oscillation, during one-half of each oscillatory cycle. Amplitude and centering control thereby obtained of the sinusoidal oscillation of the self-resonant scanner is repeatable to better than one part in ten thousand between cycles.

Abstract: A scanner for scanning an increased area of a finger held or pressed on a concave elliptically cylindrical surface having two focal axes includes a linear light source positioned at one focal axis of a first reflective cylindrical elliptical surface, the other focal axis coinciding with one focal axis of the concave elliptical surface in contact with the finger. A second reflective, cylindrical elliptical surface has two focal axes where one of the axes coincides with the position of a linear array combination of photosensitive elements and charged coupled devices and the other coincides with the other focal axis of the concave elliptical surface in contact with the finger.

Abstract: An electro-optical scanner which can write and read with common optics by using a phase hologram near the focal plane of the scanned surface.