Correction of axial deflection errors in rotating mirror systems

Correction of axial deflection in rotating mirror systems J. HELMBERGER,

K. STADLER,

errors

F. BESTENREINER

In laser beam recording systems, axial deflection errors of a polygon mirror give rise to banding patterns which recur with each scanner rotation. Experiments for compensating such errors by an additional deflection of the light beam are discussed. An economic solution was achieved by simultaneously using the acousto-optic modulator already included in the setup as a compensating deflector.

In spite of the development of efficient acousto-optic light deflectors during the last few years, high-speed laser scanners with resolutions of several thousand picture elements per line and with scanning frequencies in the kHz range are still mainly dependent on mechanical rotating mirror systems. In line-by-line image recording, extreme demands are made on the tolerances of the angles of inclination of the individual mirror facets towards the axis of rotation. The permissible angular deviation is about one second of arc. Specialist manufacturers are able to produce systems of this high accuracy. These systems, however, are extremely expensive and therefore not applicable in many cases. This paper discusses experiments in which a low-cost polygon mirror has been used for line-by-line image recording and in attempts to compensate for the errors which occur.

2. Deviations between the axis of rotation and the symmetry axis of the polygon (axial misalignment). 3. Strain due to thermal expansion of the polygon and to centrifugal forces during rotation. 4. Tolerances in the shaft bearings of the drive motor. The distribution is therefore affected by changes in temperature, speed of rotation, and operating position of the light deflector.

Face-to-0x1s ongulor error

Light - sens111ve moterlol

Focusing lens

I

Aau \ Face-to-axis angular errors

7

A collimated light beam which hits the mirror facet v deviating from its nominal inclination toward the axis of rotation by the angle J/, is thus deflected from its nominal direction by the angle 2$, (Fig. 1). When the reflected light beam is focused onto a light-sensitive material by a lens with focal length F, the face-to-axis angular error of this facet causes a line displacement in the recording of: Aa,=Ftg2$,=2F$,

Lane dlsplocement

*

mirror

1

Focal length Fig.1 Line displacement error Qu

Aa,, produced

by a face-to-axis

angular

(1)

This displacement is produced with every rotation of the polygon. If the polygon mirror has n facets, every n th line is displaced by &,. In general, such errors are not confined to one facet only. Rather, the inclination of every facet will deviate to a greater or lesser degree from that of the preceding one. This results in a periodically recurring series of line displacements and thus in a periodic interspace modulation of the lines. Fig.2 shows the distribution of deflection errors of a steel polygon with 18 facets. The errors are caused by: -20’

1. Face-to-axis angular errors of the mirror facets (machining errors). The authors are with Agfa Gevaert AG, Munich, Received 13 June 1975.

OPTICS AND LASER TECHNOLOGY.

2

3

4

5

6

7

8

3

Number

IO II of

facet

Fig.2 Distribution of the axial deflection with 18 mirror facets expressed in effective errors + u

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13

12

I4

I5

16

I7

I6

u

errors of a steel polygon face-to-axis angular

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In a printer the speed of rotation and the operating position are given features of the system and are not subject to change. The temperature of the scanner is mainly determined by the temperature of the drive motor itself and by its mounting and cooling. Due to the constant load of the motor these influences remain constant as well. A distribution of deflection errors obtained after the warming-up period therefore turned out to be very stable and could be reproduced even after weeks. Consequently, it seemed reasonable to compensate for these errors by a preprogrammed, additional deflector. The decisive factor for the practical application of this method is the expenditure involved.

Correction

Fig.4 errors.

of line displacement

The angular range of the additional deflector may be very small. In general, the deflection angles required are less than one second of arc. In high-precision systems electrooptic analogue deflectors have been used,‘T2 a method which is too expensive for simple applications. Laser scanners, however, generally include modulators for brightness control. For modulation frequencies from zero up to some MHz acousto-optic light modulators which are basically light deflectors are preferred. Bragg reflection at a travelling sound wave diffracts a portion of the incident light flux $0 into a new direction, thus forming the first order of an unsymmetrical diffraction spectrum. The deflection angle r&t is a function of the sound frequency f,:

ffd

N-

x f, Vs

where v, is the velocity of the sound wave and h the wavelength of light in the diffracting medium. The deflected

Recording PosItIon sensor Acousto-optic

t

Staircase voltage for the compensation Scale: 0.2 V cm-’

of line position

light flux #r depends on the amplitude A0 of the sound wave : 61 =

G

sin2

4

7)

with

V-A;

(3)

In a light modulator the sound frequency f, is kept constant and the light flux $1 is controlled by modulating the amplitude of the sound wave. If the acoustic frequency is also changed, the exit angle of the modulated light in the first order of diffraction changes as well and the modulator assumes the additional function of deflector. The deflection range, determined by the acoustic band width of the modulator, is generally kept small since broadband transducers are sophisticated in construction and accordingly expensive. For compensation purposes this range has to be at least twice the sum of the largest positive and the largest negative angular deviation of the facets. Fig.3 shows a diagram of the setup. The frequenciesfr to f, for the individual mirror facets can be generated in separate oscillators and transmitted to the driver stage via digitally controlled gates. In our experiments we used a voltagecontrolled oscillator (VCO) with a fairly linear voltage/ frequency characteristic in place of the n oscillators. The VCO is supplied with n voltage steps per spinner revolution with the levels of these steps corresponding to the desired deflection angles (Fig.4).

Fig.3 Block diagram of the experimental setup; fc - clock frequency, fL - line frequency, and f~ drive motor control frequency

The voltage steps are adjusted with the polygon mirror rotating at nominal speed and under simultaneous observation of the line positions in the recording plane. This is achieved by illuminating only the facet under test by the gated laser light and focusing the deflected beam onto a calibrated graticule deposited on a glass plate. Displacements of the scanning lines are observed at this scale. To eliminate laser hazards and to improve precision and speed of the adjustment procedure, the glass scale and deflected beam are imaged by a microscope onto the photocathode of a vidicon camera and observed on the screen of a black-andwhite tv home receiver. This test method discussed in [4] attains an accuracy of about f 1 second of arc.

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Stolrcose generators (18 odjustoble voltooe levels)

Clock generator I

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An essential basis for adjustment and compensation is the correct correlation between mirror facet and compensation voltage. It is achieved through synchronous control of polygon mirror drive and staircase generator. Correction

of intensity

errors

The Bragg reflection on which modulation and deflection are based, assumes its maximum value when the light beam hits the sound wave at the ‘Bragg angle’

In the case of simple, non-intersected acousto-optic transducers this means that the maximum intensity of the deflected light is reached with one acoustic frequency only. Higher and lower acoustic frequencies result in a lower luminous efficiency. If such a system is applied for light deflection, the light intensity on the borders of the deflection range decreases causing an undesirable intensity modulation dependent on the deflection angle. The error increases further if the bandwidth stage is too small.

of the driver

For compensation of the deflection errors this means that the original line displacement is eliminated but that lines with large position errors are printed with less luminous intensity. The correction of line position thus converts the former interspace modulation to an equally disturbing intensity modulation of the scanning lines. This error can be eliminated by intensity compensation. A second staircase voltage, every step of which is adjustable in level and corresponds to one mirror facet, is fed to the light modulator and controls the amplitude of the sound wave. The actual video signal, ie the voltage which determines the brightness in the image to be recorded, has to be multiplied by this compensation voltage. For adjusting the voltage levels the light is coupled out between the modulator and polygon mirror and transmitted to a photodetector whose output voltage is monitored by an oscilloscope. The modulator is supplied with the frequenciesfi to f, via the driver stage during every rotation of the polygon. Experimental

velocity is 40 cm s-l. During actual recording a metal case protects both drum and light-sensitive material frqm scattered laser light. The photodetector to the right of tne drum is only used for setting the voltage levels for the intensity compensation. The driver stage for the acousto-optic modulator and deflector, the staircase generator for both compensations, the voltage controlled oscillator, and the measurement and test equipment necessary for setting the compensation voltages are housed in a rack just behind the setup. For our tests we used a steel polygon with 18 mirror facets rotating at 114 rps. Consequently, the line frequency fr was approximately 2 kHz and the line spacing about 200 pm. The acousto-optic modulator was a ZENITH M 40-R (8 555.00) with its signal processor M 40 (# 945.00). An external carrier of about 40 MHz without amplitude modulation was applied to the signal processor input. Generally any acousto-optic modulator having the required bandwidth in modulator and drive circuits, and with a resolution time smaller than the line blanking interval can be used. Experimental

results

In order to obtain results quickly, we used Agfa Brovira Normal as the recording material. Fig.6 shows the recording of a constant gray level of medium brightness without compensation. The lines appear in the form of dark traces with light interspaces. When observing the sample in its original size, the first thing that catches the eye is a sharply defined banding pattern which recurs periodically every 3.6 mm. In the enlargement (Fig.10) it becomes evident that the cause of this error is unequal line spacing. If these line displacements are corrected (Fig.7), the banding pattern will not disappear, however. The enlargement (Fig. 11) shows clearly that the lines are now spaced equally but that they are recorded with different densities. Only an additional intensity compensation (Figs 8 and 9) eliminates the banding pattern. In the enlargements of two recordings of different gray levels (Figs 12 and 13) the lines now have the desired uniformity. A close observation reveals imperfections in compensation in these first experiments. They are mainly caused by intensity fluctuations of the laser during the setting of the compensation voltage levels. Absolute limits are set by time-variable errors and

setup

Fig.5 shows the experimental setup. The light beam, emitted by the argon-ion laser (h = 514 nm, N,,, = 3 W), in the background on the right-hand side, passes through a variable attenuator and then hits the acousto-optic modulator whose sound wave travels from top to bottom. Leaving the modulator, it splits into two partial beams. An inserted mirror deflects both beams to a mechanical shutter followed by a stop which retains the zero order beam. The first diffraction order is transmitted to the polygon mirror whose axis of rotation is orientated vertically. Line-by-line deflection thus takes place in a horizontal direction. The polygon itself is protected by a solid aluminium cover which supports the focusing lens. Two plain mirrors reflect the convergent beam in such a way that the scanning direction on the recording is vertical. A cylindrical drum - mounted to the turntable of a record player and rotating at constant angular velocity - takes over the transport of the recording carrier. The circumferential

OPTICS AND LASER TECHNOLOGY.

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Fig.5

Experimental

setup

251

Fig.6 without

Recording of a constant gray level of medium compensation (original size)

brightness

Fig.10 Microphotograph of the recording shown in Fig.6 average line spacing in the original is 200 pm

Fig.7 size)

Recording

with correction

ot line displacements

Fig.8 Recording with both corrections, level (original size)

Fig.9 Recording (original size)

with both corrections,

medium

(original

brightness

higher brightness

by errors which do not recur periodically rotation of the polygon.

The

Fig.1 1

Microphotograph

of the recording

shown in Fig.7

Fig.12

Microphotograph

of the recording

shown in Fig.8

Fig.13

Microphotograph

of the recording

shown in Fig.9

level

during every

Conclusion Our experiments have shown that it is possible and that it can be economically reasonable to compensate the axial deflection errors of a low-cost polygon mirror by using an acousto-optic light modulator as a compensating light deflector. Generally, the method will be confined to moderate-precision systems. The setup can moreover be used to simulate certain error distributions and to investigate their consequences on the recording. We would like to thank Mr Pauli and Mr Ruf for their technical assistance in preparing the experiments, and Miss Krabbe for translating the manuscript. References 1 2

3 4

Bousky, S., Teeple, L. Laser Recorder for I:ourier Processing, SPSE Technical Conference (New York, May 6-l 1, 1973) Taneda, T., Sato, T., Tatuoka, S., Alko, M., Masuko, H. JSMPTE 82 (1973) 470-474 Gordon, E. I. ProcIEEE 54 (1966) 1391-1401 Helmberger, J., Stadler, K., Bestenreiner, F. 0ptik 4 1 (1974) 402-409

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