Abstract: A laser scanning device includes a polygon mirror, one or more lenses, and a plurality of light shielding plates. The polygon mirror reflects a light beam during rotation of the polygon mirror. The lenses allow the light beam reflected off the polygon mirror to pass through the lenses. The plurality of light shielding plates are arranged at a distance from each other and block an undesirable beam, which is part of the light beam, reflected off at least one of the lenses and heading for an optical device. The plurality of light shielding plates form an air channel that allows an air current generated by the rotation of the polygon mirror to flow through the air channel.

Abstract: An image forming apparatus includes plural photosensitive members, a scanner unit for scanning the photosensitive members, and a fixing unit for fixing toner images. The scanner unit includes a rotatable polygonal mirror for reflecting laser beams emitted in correspondence to respective photosensitive members, reflecting members for reflecting the laser beams, and a box for accommodating the polygonal mirror and the reflecting members. The box includes plural outlets for the laser beams. Of the reflecting members, first and second reflecting members reflect laser beams toward corresponding first and second outlets respectively positioned farthest from and closest to the fixing unit.

Abstract: Aspects of the technology employ sensors having high speed rotating mirror assemblies. For instance, the sensors may be Lidar sensors configured to detect people and other objects in an area of interest. A given mirror assembly may have a triangular or other geometric cross-sectional shape. The reflective faces of the mirror assembly may connect along edges or corners. In order to minimize wind drag and torque issues, the corners are rounded, filleted, beveled, chamfered or otherwise truncated. Such truncation may extend the length of the mirror side. The mirror assembly may employ one or more beam stops, light baffles and/or acoustic/aerodynamic baffles. These sensors may be employed with self-driving or manual driven vehicles or other equipment. The sensors may also be used in and around buildings.

Abstract: A system for use in identifying a user includes a portable emitter transported with the user. The emitter includes a quantum cascade laser configured to emit a thermal beam identifying a location of the user in response to a command, the thermal beam having a wavelength between approximately 2 ?m and approximately 30 ?m.

Abstract: Image plane registration errors are corrected for a multi-channel printing system that prints on a continuous web of media. Nominal in-track line spacing are defined for each image plane, and are used to print lines of image data for each image plane. An in-track registration error is measured for a misregistered image plane in the printed image, and is used to determine an adjusted in-track line spacing that will bring the misregistered image plane back into registration in the in-track direction over a predefined correction time interval. Additional image data is then printed using the adjusted in-track line spacing during the correction time interval, after which image data is printed using a new in-track line spacing that is different from the adjusted in-track line spacing.

Abstract: Disclosed embodiments provide laser object marking methods and devices in which multiple slidable mechanisms are used for holding respective laser heads.

Abstract: In a scanning optical apparatus including a light source, a light deflector having a reflecting surface, and a single scanning lens, a light flux deflected in a main scanning direction is focused on an image surface. The reflecting and image surfaces are conjugate to each other with respect to a sub scanning direction, Bmax×Bmin>0, and Dmax×Dmin<0 where Bmax and Bmin are a maximum value and a minimum value, respectively, of paraxial focal points, Dmax and Dmin are a maximum value and a minimum value, respectively, of midpoints of focal depth in the sub scanning plane, the values being determined with reference to the image surface, wherein the value of the image surface is 0 and the values on a farther-from-the-scanning-lens side behind the image surface have positive values.

Abstract: An improved particle effect projector is disclosed that reduces the energy density of a laser beam projected through a movie theater or other entertainment venue, comprising an F-theta lens, a beam expander and a beam focuser with a long focal length that approximates the distance between the particle effect projector and the movie screen or other surface onto which the particle effect beam is being projected.

Abstract: A 2-D scanning system uses a fast-rotating raster-polygon as a single scanning component to produce straight scan lines over a 2-D image surface. An approach angle of incident light beams to the raster-polygon is selected to minimize pin-cushion distortion of scan lines introduced by polygon scanning on the image surface, and a tilt angle of the rotational axis of the raster-polygon is selected to position said polygon-scanning distortion symmetrically on the image surface. In addition, scan optics are configured to generate a predetermined amount of barrel distortion of scan lines on the image surface to compensate for pin-cushion distortion introduced by polygon scanning.

Abstract: An optical writing device includes a light source, an optical deflector that deflects and scans light from the light source, a pre-deflector optical system that guides the light from the light source to the deflector, a post-deflector optical system that guides the scanned light to a target surface, a cover covering the deflector and including a first opening and a second opening provided at different positions, and a housing housing these optical elements. Light traveling from the light source to the deflector and the light scanned by the deflector are transmitted through the first opening but not through the second opening. During the rotation of the deflector, a forced inflow of air flowing from outside to inside the cover is generated in the first opening, and a discharged airflow flowing from inside to outside the cover is generated in the second opening.

Abstract: An optical scanning apparatus includes a light source; and a rotational polygon mirror having N reflecting surfaces, the rotational polygon mirror being configured to reflect a light flux emitted from the light source so that a scanning surface is scanned along a main-scanning direction with reflected from the rotational polygon mirror. A width of the light flux incident on the rotational polygon mirror in a direction corresponding to the main-scanning direction is smaller than a width of each reflecting surface of the rotational polygon mirror in the direction corresponding to the main-scanning direction.

Abstract: A light scanning unit and an electro-photographic image forming apparatus employing the same are provided.

Abstract: A light beam emission apparatus separates, via a half mirror, apart of a laser beam emitted from a semiconductor laser towards a photosensitive member, guides the separated laser beam to an optical sensor to detect a light quantity, and controls the light quantity based on the detected result. The light beam emission apparatus includes a first light blocking member located between the semiconductor laser and the half mirror, and a second light blocking member located between the half mirror and the optical sensor.

Abstract: An optical scanning device includes a housing, a laser light source outputting a laser light, a polygon mirror arranged in an arrangement space and deflecting the laser light to scan a predetermined object with the laser light while rotating, a polygon motor rotating the polygon mirror, a control board arranged in the arrangement space and controlling the polygon motor, and a flow-control member arranged in the arrangement space and guiding an airflow generated by a rotation of the polygon mirror to an outside of the arrangement space to circulate the airflow within the housing.

Abstract: A light scanning unit and an electrophotographic image forming apparatus are provided. The light scanning unit includes a light source emitting the light beams according to an image signal, an incident optical system including a flux-limiting element limiting the flux of light beams emitted by the light source, an optical deflector deflecting the light beams emitted by the light source in a main scanning direction, and an image forming optical system including a scanning optical element imaging the light beams deflected by the optical deflector on a scanning target surface, the light scanning unit forming an electrostatic latent image by scanning the light beams to the scanning target surface of the image bearing member. The scanning optical element of the scanning optical elements of the image forming optical system is eccentrically arranged from a central optical axis of the image forming optical system in a sub-scanning direction.

Abstract: An optical scanning device includes a pre-deflection optical system including a first optical element that adjusts the shape of beams emitted from the light source; and a second and third optical elements arranged such that the second optical element is arranged closer to the light source than the third optical element is. Both of the second and third optical elements have no refracting power in the deflection scanning direction and have positive refracting power only in a direction perpendicular to the deflection scanning direction. An interval between scanning lines formed on the scanned area and a deviation of the scanning-line interval between scanning positions are adjusted by displacement of the second and third optical elements in a direction of an optical axis of the pre-deflection optical system and displacement of at least one of the second and third optical elements in the direction perpendicular to the deflection scanning direction.

Abstract: An optical scanning device has a light deflector deflecting a light beam from a light source, a synchronization detection sensor determining timing of starting scanning in main scanning direction based on timing of detecting the light beam scanned in main scanning direction by the light deflector, and a pre-sensor imaging optical system imaging the light beam reflected from the light deflector on the synchronization detection sensor. The pre-sensor imaging optical system moves the imaging position of the light beam on the synchronization detection sensor in a direction making the timing of detecting the light beam earlier or later according to whether variation in temperature causes the magnification of the scanning optical system in main scanning direction to increase or decrease respectively.

Abstract: An optical scanning device includes a plurality of stations, each of which includes an light source, a deflector (polygon scan), a scanning optical element, and a housing. The light source emits a light beam to a plurality of surfaces to be scanned. The deflector deflects light beams emitted from the light source. The scanning optical element scans the surfaces to be scanned with light spots of the optical beams deflected by the deflector. The housing houses therein the light source, the deflector, and the scanning optical element. The scanning optical element is secured to the housing so that directions of scanning-line curves caused by temperature change match between the surfaces to be scanned.

Abstract: The image forming apparatus includes a determination unit configured to determine whether or not a polygon mirror has converged to the number of rotations that allows image formation to be performed, and the determination unit is capable of detecting a first timing and a second timing and determines that the polygon mirror has converged to a number of rotations that allows the image formation to be performed based on an earlier one of the first timing and the second timing.

Abstract: An optical scanning apparatus includes a light source configured to emit a light beam, a scanning unit configured to deflect the light beam from the light source so as to scan a photosensitive member, an optical lens configured to guide the light beam scanned by the scanning unit onto the photosensitive member, and a lens supporting unit having a fixing portion configured to fix the optical lens, wherein the lens supporting unit includes a movable supporting portion configured to restrict movement of the optical lens in a direction perpendicular to a scanning direction of the light beam and an optical axis direction of the optical lens, to restrict movement of the optical lens in the optical axis direction, and to support the optical lens movably in the scanning direction.

Abstract: An image forming apparatus includes an image forming unit which transfers an image obtained through exposure and development to paper, and a control unit which changes a rotation speed of a polygon mirror at an intermediate area on a carrier to change a reduction/magnification ratio of an image. The control unit changes the rotation speed in a stepwise manner in such a way as to allow a stable rotation of the polygon mirror in each step, and controls the image forming unit to form a corrected patch image in parallel with the stepwise change of the rotation speed. The corrected patch image is obtained through correction in accordance with the stepwise change of the rotation speed to be the same as the patch image formed when the rotation speed is not changed.

Abstract: The calculation unit calculates the time interval between the time at detecting the light beam reflected by the reflective surface of the rotatory polyhedron incident on the BD sensor by the light beam detecting unit and the time at detecting the light beam reflected by the reflective surface incident on the optical sensor in the light source by the return light beam detecting unit. The scan adjusting unit adjusts the luminescence time of the light source for scanning the light beam on the surface to be scanned based on the time interval calculated by the calculation unit.

Abstract: An optical scanning device includes: a light source unit; a light deflecting unit that deflects a light beam emitted from the light source unit; a scanning optical device that focuses the light beam deflected by the light deflecting unit on a scanned surface; and a light shielding member. The scanning optical device is provided in a direction in which a sound pressure level of a noise caused by rotation of a rotating polygon mirror included in the light deflecting unit is highest.

Abstract: If inclination correction of scanning line is performed while the incident position of the laser beam is not suitable, the shape of a spot of the laser beam which forms an image on a photosensitive drum may not be uniform depending on the scanning position of the laser beam. The housing is provided with a U-shaped groove to which the convex portion of a lens hold member that holds the lens is engaged. With the position of the convex portion adjusted, the convex portion is attached and secured in the U-shaped groove. Thus, the installation position of the lens to an optical path of the laser beam is adjusted, and the lens can be rotated and adjusted in order to correct an inclination or a bending of scanning line.

Abstract: A light scanning unit and an electrophotographic image forming apparatus employing the same. The light scanning unit includes an imaging optical system including, when a path of one of the light beams directed to one of the surfaces disposed relatively far from the deflector is referred to as a first light path and when a path of one of the light beams directed to one of the surfaces disposed relatively close to the deflector is referred to as a second light path, light paths in which both of a section of the second light path before a first change of the second light path and a section of the second light path after the first change of the second light path intersect a section of the first light path after a second change of the first light path.

Abstract: A polygon mirror assembly, a light scanning unit employing the polygon mirror assembly, and an image forming apparatus. The polygon mirror assembly includes a polygon mirror formed of a plastic material and having a plurality of reflection surfaces; and a motor unit to support and rotate the polygon mirror, where the polygon mirror is coupled to the motor unit by using an adhesive material.

Abstract: An optical scanning device includes a light source that emits a laser beam, a deflector that deflects the emitted laser beam, a scanning lens that causes the deflected laser beam to scan a surface of a photosensitive body at a uniform velocity, a reflector having a reflective surface that reflects the deflected laser beam toward the photosensitive body among the laser beams that have passed through the scanning lens, and a synchronization sensor that receives the laser beam from the reflector and outputs a detection signal. The reflector is set so that a scanning speed in a main scanning direction of the laser beam on a light-receiving surface of the synchronization sensor becomes greater than a value obtained by dividing a scanning distance of the laser beam in the main scanning direction on the light-receiving surface of the synchronization sensor by a response delay time of the synchronization sensor.

Abstract: An optical scanning device includes a MEMS mirror, a driving unit for oscillating the MEMS mirror using a drive voltage which varies in a basic cycle, a light detection unit for receiving laser light deflected by the MEMS mirror and outputting a detection signal, a correction value calculation unit for calculating a correction voltage value used in correcting the drive voltage, a DC voltage generation unit for generating a DC voltage having a voltage value smaller than the correction voltage value, a DC voltage amplification unit for amplifying the DC voltage generated by the DC voltage generation unit to have a voltage value equal to the correction voltage value, and a waveform shaping unit for shaping the waveform of the amplified DC voltage so that the DC voltage varies in the basic cycle and outputting the shaped DC voltage as the drive voltage to the driving unit.

Abstract: An optical scanning apparatus, including: a light source; an incident optical system; and an imaging optical system, in which: the imaging optical system includes at least one plastic lens; in a sub-scanning section, principal rays of the beams intersect each other on an optical axis of the imaging optical system; the principal rays intersect each other at different positions between a case of entering a central region of the at least one plastic lens and a case of entering an end region of the at least one plastic lens; and the principal rays entering one of the central region and the end region of the at least one plastic lens intersect each other, and the principal rays entering another of the central region and the end region of the at least one plastic lens intersect each other.

Abstract: An optical scanning device includes a polygon scanner that deflects and scans light beams, a body on which the polygon scanner directly mounted, and a heat dissipating unit that dissipates heat of the deflection scanning unit. The heat dissipating unit is located at a position on an outer surface of the body corresponding to the deflection scanning unit. The body is provided with a pair of wall portions on the outer surface. The wall portions face each other with the heat dissipating unit between them, and extend in a direction in which air blown by an air blowing unit flows to form an air-flow path.

Abstract: A visible laser beam scanned by a galvano-scanner system is aligned at each of positioning points on the top surface of a master work by manual operation to record sensor position signals of position sensors on galvano-scanners. The sensor position signals on each positioning point are recorded to create a drive pattern in accordance with recorded sensor position signals. The drive pattern no longer has optics system error sources including focus error and attachment error as well as errors caused by scale, offset and the like, also eliminating the need for entering a distance as far as the top surface of the work. Therefore, the drive pattern with error components removed can be created with ease.

Abstract: An optical scanning apparatus for scanning a target surface using a plurality of light beams simultaneously along a first direction of the target surface. The apparatus has a light source having a plurality of light emitting elements; an optical deflector to deflect the plurality of light beams coming from the light source; and a scanning optical system to guide the plurality of light beams deflected by the optical deflector to the target surface. The scanning optical system includes a lens, disposed after the optical deflector, having the strongest power in a second direction perpendicular to the first direction. A plurality of scan lines, corresponding to the plurality of light beams deflected by the optical deflector, intersect or contact each other at an optical face of the lens.

Abstract: In a light source device including an aperture member that regulates a light beam, |(Pap1?Pap2)/Pap2|<|(P1?P2)/P2| is satisfied where P2 is a light intensity of the light beam entering the aperture member at a time t2 when 2 microseconds have passed since current was applied to the laser, P1 is a light intensity of the light beam entering the aperture member at a time t1 when 40 nanoseconds have passed since a light intensity of the light beam entering the aperture member reached 0.1 time the light intensity P2, Pap2 is a light intensity of the light beam output from the aperture member at the time t2, and Pap1 is a light intensity of the light beam output from the aperture member at a time t1? when 40 nanoseconds have passed since a light intensity of the light beam output from the aperture member reached 0.1 time the light intensity Pap2.

Abstract: Disclosed are a light scanning unit and an electrophotographic image forming apparatus including the light scanning unit. The light scanning unit may include a light source emitting a light beam, a beam deflector that deflects and scans the light beam emitted from the light source in a main scanning direction, a scanning optical system forming an image of a first portion of the light beam that is deflected and scanned by the beam deflector on a scanning surface and a beam detection sensor receiving a second portion of the light beam that is deflected and scanned by the beam deflector for generating a synchronization signal. The beam detection sensor may include a light receiving surface for receiving the second portion of the light beam, and at least two output terminals that are arranged outside an area of the light receiving surface within which the incident second portion of the light beam is confined.

Abstract: A laser light irradiating system which irradiates a laser light onto a thermally reversible recording medium which is pasted on a face on one side of an object to be conveyed to perform one of image erasing and image recording is disclosed. The laser light irradiating system includes a conveying unit; a detecting unit; a laser light emitting unit; and a control unit, wherein the control unit conveys the object to be conveyed to a specific position and, when the thermally reversible recording medium is not detected by the detecting unit, the laser light with a power level greater than or equal to a predetermined power level is prevented from being emitted from the laser light emitting unit.

Abstract: A laser rewriting apparatus positioned on one side or the other side of a conveyance path through which a to-be-conveyed object on which a thermoreversible recording medium is affixed is conveyed in a predetermined conveyance direction. The laser rewriting apparatus emits laser light to the thermoreversible recording medium and rewrites an image. The laser writing apparatus includes an image erasing apparatus that emits laser light to the thermoreversible recording medium and erases the image from the thermoreversible recording medium; and an image recording apparatus positioned on the predetermined conveyance direction downstream side of the image erasing apparatus and records a new image by emitting laser light to the thermoreversible recording medium. The image erasing apparatus and the image recording apparatus have the respective laser light emitting parts from which the laser light is emitted at ends on the same side with respect to the predetermined conveyance direction.

Abstract: According to one embodiment, an optical scanning device includes plural light sources, a polygon mirror, a first lens, a first reflection mirror, and a second lens. The polygon mirror deflects lights emitted from the plural light sources in a predetermined direction. The first lens allows the lights emitted from the plural light sources and deflected by the polygon mirror to pass. The first reflection mirror reflects the lights passed through the first lens in a direction different from the deflecting direction of the polygon mirror. The second lens receives incidence of the lights reflected by the first reflection mirror from a direction different from an incident direction of the first lens and allows, with one lens, the lights emitted from the plural light sources to pass.

Abstract: An optical scanner includes: a light reflecting section having light reflectivity; a movable section which includes the light reflecting section and can be displaced; two link sections connected to positions of ends of the movable section, the positions facing each other; a supporting section supporting the link sections; and a displacement providing section turning the two link sections, wherein each link section includes a turnable drive section, and a shaft section connecting the movable section and the drive section and bending in a thickness direction of the movable section by turning of the drive section.

Abstract: An optical writer includes a light source, an optical part, a housing, and an elastically deformable retainer. The light source projects light against a target. The optical part is disposed on a light path between the light source and the target. The housing houses the light source and the optical part. The elastically deformable retainer is detachably fixed to the housing and includes a plurality of contact portions on an inner surface of the retainer to hold the optical part. The retainer elastically deforms to separate at least one of the contact portions from other contact portions to hold the optical part by the plurality of contact portions.

Abstract: An image forming apparatus includes a scanning optical device which performs scanning on a photosensitive drum with laser light. The scanning optical device includes a polygon motor unit, an emergence unit and a projecting unit. The polygon motor unit includes a polygon mirror which performs the scanning on the photosensitive drum with the laser light emitted from a light source. The laser light emerges from the emergence unit so that the photosensitive drum is irradiated with the laser light. The projecting unit projects to a first side where the photosensitive drum is disposed from a partition wall. The polygon motor unit is disposed in the projecting unit. The emergence unit is disposed on a second side separated from the first side by the partition wall. A gap is provided between the partition wall and the scanning optical device.

Abstract: An optical scanning apparatus and an image forming apparatus having the optical scanning apparatus includes a before-light-deflecting-unit optical system and a scanning optical system. The optical system includes a first optical device, a second optical device made of a resin material which has an anamorphic negative refracting power in a deflection scanning direction and a deflection scan perpendicular direction and has a larger refracting power in the deflection scan perpendicular direction than a refracting power in the deflection scanning direction, and a third optical device made of a glass material which has substantially no refracting power in the deflection scanning direction and a positive refracting power in the deflection scan perpendicular direction. An interval of the scanning lines formed on the scanned surface is adjusted by displacement of the second and third optical devices in an optical axis direction of the before-light-deflecting-unit optical system.

Abstract: An optical scanning unit may include a light source unit configured to emit a light beam, an optical housing configured to receive and support the light source unit, an optical device configured to deflect the light beam and to focus the light beam on a light receiving member, and a fixing member configured to fix the light source unit to the optical housing by applying pressure to the light source unit, wherein the pressure is applied in a direction, which is substantially perpendicular to an optical axis direction of the light source unit.

Abstract: An optical scanning apparatus has first and second light sources, a deflection scanning device, and first and second scanning optical systems that guide the first and second laser beams deflected for scanning by the deflection scanning device. The first and second scanning optical systems include scanning lenses and a polarization beam splitter arranged in a downstream side of an optical path of the scanning lens, the first scanning optical system including a half-wave plate arranged in the downstream side of the optical path of the scanning lens and in an upstream side of an optical path of the polarization beam splitter, the first laser beam and the second laser beam having different phases by 180 degrees from each other before being incident on the first and second scanning optical systems.

Abstract: According to one embodiment, if it is designated by operation of a control panel that a printed halftone image for test is defective, a number of revolutions of a polygon mirror is finely adjusted by a predetermined rate and a frequency of a serial data signal is finely adjusted by the rate.

Abstract: A plurality of light sources, a light deflector, and a single scan lens. The light deflector deflects a plurality of light beams emitted from the light sources by a same face for scanning a plurality of to-be-scanned portions simultaneously. The single scan lens receives the light beams from the light deflector and focuses the light beams onto each of the plurality of to-be-scanned portions to scan the to-be-scanned portions simultaneously. The single scan lens is used in common for the light beams, and has one incidence plane and a plurality of exit planes in a sub-scanning direction separately prepared in the sub-scanning direction for each of the to-be-scanned portions. The incidence plane has a refractive power of the lens in the sub-scanning direction decreasing toward peripheral portions in the main scanning direction. The exit planes have positive refractive power in the main and sub-scanning directions.

Abstract: An optical imaging apparatus (80) for direct engraving of flexographic plates (52) includes at least two laser sources (43), each emitting laser beams (44). A mirror or prism (45) is placed in front of each of the laser sources to alter an optical path of each of the laser beams. The laser beams cut the flexographic plate at different depths and cut out chunks (65) of the flexographic plate.

Abstract: A light sensor generates a detection signal upon receiving laser light. A rotation sensor generates a rotation signal in synchronization with rotation of a polygon motor. A mirror-rotation-signal generating section generates a mirror rotation signal, based on the detection signal. A motor-rotation-signal generating section generates a motor rotation signal, based on the rotation signal. A phase-difference measuring section measures a phase difference between the motor rotation signal and the mirror rotation signal. A prediction-signal generating section generates a prediction signal that is delayed from the motor rotation signal by the phase difference. A switching section switches a control mode between: a mirror control mode in which the mirror rotation signal is used to control a rotational speed of the polygon mirror; and a prediction control mode in which the prediction signal is used to control the rotational speed. A motor driver drives the polygon motor in the selected control mode.

Abstract: A scanning optical apparatus includes scanning units, a deflector. Each of the apparatuses includes a light source, an imaging optical system including imaging optical elements imaging a beam deflected by the deflector on a scanning surface. The scanning surfaces are scanned with beams in opposing directions. When a main scanning direction of the first scanning unit is a Y positive direction, a sign is the same between ?1h(Y1min)×?1r and ?2h(Y1min)×?2r. Here, ?1h(y), ?2h(y) denote orientation angles between the Y axis and a slow axis at a Y direction position y of first/second imaging optical elements from an optical axis, the imaging optical elements each being an imaging optical element having a largest thickness among them of the imaging optical systems, ?1r and ?2r denote angles between the Y axis and polarization directions of the beams reaching the imaging optical elements, and Y1min denotes a Y position where ?1h(y) becomes minimum.

Abstract: Raster Output Scanners and printing systems are presented along with methods for mitigating banding in printing systems, in which electronic banding compensation is employed using cross-process direction light source intensity banding correction profiles tailored to corresponding reflective facets of a rotating polygon.

Abstract: In a scanning optical apparatus, an illumination optical system has a diffractive power ?dM and a refractive power ?nM in a main scanning direction, and a ratio ?nM/?dM in the main scanning direction for a focal length fi in a range of 10-22 mm satisfies: g2(fi)??nM/?dM?g1(fi), where A(Z)=(1.897×107)Z2+6744Z+0.5255, B(Z)=(2.964×107)Z2+5645Z+0.6494, C(Z)=(3.270×107)Z2+3589Z+0.5250, D(Z)=(5.016×107)Z2+4571Z+0.8139, g1(fi)=fi{D(Z)?B(Z)}/12?5D(Z)/6+11B(Z)/6, g2(fi)=fi{C(Z)?D(Z)}/12?5C(Z)/6+11A(Z)/6 g2(fi)=fi{C(Z)?A(Z)}/12?5C(Z)/6+11A(Z)/6.