WO1988008997A1 - Ameliorations apportees a la modulation d'un faisceau lumineux - Google Patents

Ameliorations apportees a la modulation d'un faisceau lumineux Download PDF

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Publication number
WO1988008997A1
WO1988008997A1 PCT/US1988/001450 US8801450W WO8808997A1 WO 1988008997 A1 WO1988008997 A1 WO 1988008997A1 US 8801450 W US8801450 W US 8801450W WO 8808997 A1 WO8808997 A1 WO 8808997A1
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WO
WIPO (PCT)
Prior art keywords
frequency
laser diode
etalon
light
current
Prior art date
Application number
PCT/US1988/001450
Other languages
English (en)
Inventor
Paul Bernard Mauer
Badhri Narayan
James Edward Roddy
Original Assignee
Eastman Kodak Company
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Eastman Kodak Company filed Critical Eastman Kodak Company
Publication of WO1988008997A1 publication Critical patent/WO1988008997A1/fr

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Classifications

    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S5/00—Semiconductor lasers
    • H01S5/06—Arrangements for controlling the laser output parameters, e.g. by operating on the active medium
    • H01S5/062—Arrangements for controlling the laser output parameters, e.g. by operating on the active medium by varying the potential of the electrodes
    • H01S5/06209—Arrangements for controlling the laser output parameters, e.g. by operating on the active medium by varying the potential of the electrodes in single-section lasers
    • H01S5/06213—Amplitude modulation
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/21—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference
    • G—PHYSICS
    • G02—OPTICS
    • G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
    • G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
    • G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour 
    • G02F1/21—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour  by interference
    • G02F1/213—Fabry-Perot type
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S5/00—Semiconductor lasers
    • H01S5/06—Arrangements for controlling the laser output parameters, e.g. by operating on the active medium
    • H01S5/062—Arrangements for controlling the laser output parameters, e.g. by operating on the active medium by varying the potential of the electrodes
    • H01S5/06209—Arrangements for controlling the laser output parameters, e.g. by operating on the active medium by varying the potential of the electrodes in single-section lasers
    • H01S5/0622—Controlling the frequency of the radiation

Definitions

  • This invention relates to modulation of the intensity of the beam of light, having at least a degree of coherence, derived from a source, such as a laser diode, whose emission frequency varies with the nature of the electrical energy supplied to the source.
  • Proposals for modulating the intensity of light beams derived from laser diodes have included modulation of the light before it exits the diode and modulation of the beam after it exits the diode.
  • the former has been termed internal modulation and the latter has been termed external modulation.
  • internal modulation has involved variation of the electrical current applied to the laser diode.
  • the wavelength of the light emitted by a laser diode is dependent on the current .applied to the diode. It is believed that such dependency is due to at least two causes. Firstly, that the refractive index of the optical cavity of the laser diode is dependent on current density and temperature. Secondly, the temperature, and hence length of the optical cavity, varies with current density.
  • the intensity modulation is accompanied by a frequency change and if the intensity modulation is sufficiently large as to be useful then the frequency change will also be large.
  • Such large frequency changes can be very undesirable in such uses of the laser diode as in a dispersive optical syste , e.g. as a transmitter in a fiber optic communication system, and as in a diffractive optical system, e.g. as a light source in a writing scanner including, as a diffractive element, a hologon.
  • U.S. Patent Specification No. 4,638,483 describes a modulatable light generator including means for producing a collimated beam of light having at least a degree of coherence, including a light source.
  • the light source is adapted to vary its emission frequency in dependence on the nature of the electrical energy supplied to it by the drive means.
  • the drive means is adapted to vary the nature of the electrical energy supplied to the light source by an amount large enough to cause a change in frequency of the output beam to change the interference in the interferometer.
  • the interferometer is a Michelson or Mach-Zehnder •interferometer or it is a fiber optic recirculating loop.
  • Michelson and Mach-Zehnder ' " interferometer embodiments there is no ability to select the finesse of the output.
  • fiber optic embodiment of Fig. 5 of U.S. 4,638,483 there is some, but limited, ability to select finesse.
  • Finesse is defined as the ratio of the passband separation to the width of the passband. Disclosure of the Invention
  • the problems of the prior art are overcome by the present invention by using a Fabry-Perot interferometer for converting from frequency modulation to intensity modulation.
  • the Fabry-Perot interferometer allows selection of the finesse by appropriate choice of the reflectivity of the reflective coatings.
  • the light source is a laser diode and the nature of the electrical energy which the drive means is adapted to vary is the magnitude of the current of the electrical energy supplied to the laser diode.
  • Many laser diodes are capable of causing the frequency of the output beam to change by jumping and drifting between jumps as the current supplied to them varies in magnitude.
  • the drive means may be adapted to vary the magnitude of the current supplied to the laser diode by an amount less than the current variation needed to cause the drift between successive jumps. In this way, the frequency may be shifted by drifting between a frequency at which destructive interference occurs in the interferometer and another frequency at which constructive interference occurs, without causing a jump in frequency.
  • the drive means is adjustable so that the current supplied to the laser diode is such as to cause the laser diode to emit light at a frequency approximately at the middle of the region of drift.
  • the drive means may be adapted to vary the magnitude of the current of the electrical energy supplied to the laser diode by an amount less than that necessary to cause the frequency to vary from the aforementioned frequency at the middle of a region of drift to a frequency at which a jump in frequency occurs at an end of said region of drift.
  • the etalon may include a transmissive plate having opposed parallel faces and reflective coatings on the opposed faces.
  • the reflective coatings have a high reflectance whereby the passbands of the etalon are narrow.
  • the reflectance of the reflective coatings may be low whereby the passbands of the etalon are broad.
  • Fig. 1 is a plot of optical output power against forward current for a typical laser diode
  • Fig. 2 is a plot of lasing peak wavelength against forward current for a typical laser diode
  • Fig. 3 is a plot of the normalized intensity of two adjacent passbands of a Fabry-Perot etalon
  • Fig. 4 is similar to Fig. 3 but includes four curves, one for each of four different reflectances of the reflective surfaces of the etalon;
  • Fig. 5 is a schematic representation of a writing holographic scanner including a modulatable light source in accordance with the present invention
  • Fig. 6 is a schematic representation of a cross-section of a Fabry-Perot etalon. Best Mode of Carrying Out the Invention
  • the light source is a source of coherent light and is a laser diode and the nature of the electrical energy which is varied and supplied to the light source is the magnitude of the current.
  • Fig. 1 is a plot of the optical output power P n against forward current I Cincinnati for a typical laser diode.
  • the curve 20 has a low slope portion 22 and a greater slope portion 24.
  • the curve portion 22 is the spontaneous emission region and the curve portion 24 is the lasing region.
  • the curve demonstrates that the optical output power of a laser diode increases with forward current. It is known to modulate a laser diode by varying the forward current. For example, with a particular laser diode which has a threshold current It.,h of
  • Fig. 2 is a plot, for an exemplary laser diode, of the variation in wavelength ⁇ with variation in forward current ! _.. Variation in forward current causes a change r in the refractive index of the active cavity and in the physical length of the cavity, both of which affect the effective path length of the cavity, which in turn controls the wavelength of the output beam.
  • the jumps 26 are of about 0.3 nm and the frequency change in a drift is at a rate of about 0.0075 nm per milliampere. While the extents of the drift regions vary, there are drift regions 28 which extend for about 20 mA, that is, the current can be changed by about 20 mA after one jump, before the next. Some drift regions in some laser diodes may be substantially bigger.
  • Fig. 6 illustrates a cross-section of a Fabry-Perot etalon 30, which comprises a transparent plate 32 having planar, parallel opposed surfaces 34 which have reflective coatings 36.
  • the coatings 36 are partially transparent to allow an incident beam 38 to enter the etalon and to allow a beam 40 to leave the etalon 30.
  • the coatings are also reflective to light incident on them at the interfaces with the plate 32 so that they internally reflect a portion of the light in the plate 32. It is.known that the pathlength of the light beam within the plate 32 determines, for a particular wavelength, whether there is constructive or destructive interference and hence determines, in part, the fraction of the energy in the input beam which appears in the output beam.
  • the effective pathlength within the plate 32 is, of course, dependent on the physical thickness of the plate, which is in turn dependent on temperature; on the refractive index of the material of the plate; and on the angle of incidence of the input beam 38. If these three parameters, thickness, refractive index, and incidence angle, are kept constant, and the wavelength of the incident light is varied, then the intensity of the output beam 40 will vary as the frequency of the incident beam 38 is varied. Thus, with the incident beam 38 being the collimated output beam of a laser diode, the intensity of the output beam 40 is dependent on the frequency of the light emitted by the diode.
  • Fig. 3 is a plot of the normalized intensity of the transmitted light against phase difference ⁇ , which is related to wavelength.
  • the actual intensity of the output beam relative to the input beam is dependent on the transmittance of the reflective coatings 36.
  • the transmittance and the reflectance are inversely dependent on one another.
  • Fig. 4 shows a plurality of plots, each similar to Fig. 3, but for different values of reflectance R of the coatings. It will be observed that the contrast between "on” and “off” decreases with decreasing reflectance and the width of the "on" passbands increases with decreasing reflectance.
  • the design and construction of etalons to achieve required performance characteristics is believed to be sufficiently well understood by those skilled in the art that further description herein is deemed unnecessary.
  • the parameters important to satisfactory performance of the etalon in the present context are: peak transmission; width of the passband; and the separation of the passbands. Finesse, the ratio of the passband separation to the width of the passband, is used as a measure of the tunability of the etalon.
  • n index of refraction of etalon
  • FIG. 5 is a schematic representation of a holographic writing scanner embodying a modulatable light source in accordance with the present invention. Laser scanners are well known and only those features necessary for an understanding of the present invention will now be described. It is to be understood that other features not described and necessary for the scanner to function may be derived from the art.
  • the scanner includes a transparent disc 50 having thereon a plurality of sector-shaped facets each containing, in known manner, identical diffraction gratings with the lines of the gratings being tangential.
  • the disc 50 is mounted on the shaft 52 of a motor 54 controlled for rotation at constant speed by a controller 55.
  • a laser diode 56 has a divergent output beam 58 which is " co limated by a collimator 60 into a collimated beam 62.
  • the collimated beam 62 is directed at the disc 50.
  • the Fabry-Perot etalon 30 Between the collimator 60 and the disc 50 and in the collimated beam 62, there is the Fabry-Perot etalon 30. In the present embodiment the angle of incidence of the beam on the etalon is close to normal.
  • the diffracted beam has the reference numeral 64 in Fig. 5.
  • the diffracted, scanning beam 64 is incident on an f ⁇ lens 66 which serves to focus the beam onto the surface of a drum 68 about which is wrapped a web 70 of photosensitive material.
  • the etalon 30 is provided with a device 80 for keeping the etalon at constant temperature.
  • the device 80 is controlled by a control device 82.
  • a signal source 72 constituting drive means for the laser diode, supplies electrical energy to the light source and controls the nature of that energy. With the light source being a laser diode in the present embodiment, it is the current which the signal source 72 controls.
  • the forward current supplied to the laser diode 56 by the signal source has an instantaneous magnitude related to the signal desired to be applied by the light beam to the photosensitive web, i.e. the current is of one of two values depending on whether the beam is to be "on" or "off".
  • the laser diode 56, the collimator 60 and the etalon 30 constitute a modulatable light generator in accordance with the present invention.
  • the frequency of the beam output by the laser diode is dependent on temperature. It may be found necessary to stabilize the diode against temperature drifts occurring due, for example, to ambient conditions or due to relatively long term heating of the diode by the applied forward current. Such temperature changes may be regarded as long term and are to be distinguished from the instantaneously occurring temperature changes in the junction of the diode due to variations in the forward current. Such instantaneously occurring changes are acceptable and, indeed, are part of the mechanism for causing small frequency changes, in accordance with the invention.
  • Fig. 5 shows a temperature stabilizing means 74, in the form of a thermoelectric cooler, and its controller 76, for controlling and stabilizing the temperature of the diode 56. _
  • the current I_ D applied by the signal source 72 is selected not only so that the beam 58 has the desired intensity but also so that the frequency of the beam is approximately at the middle of a drift region 28, - i.e. it is approximately equally spaced from the adjacent jumps 26. (see Fig. 2).
  • This middle, position is chosen so that a maximum change in frequency, either up or down, can be accommodated without a frequency jump being encountered. Let it be assumed that at that mid point the frequency is such that there is constructive interference in the etalon. If the current is now varied incrementally up or down to I_, the frequency of the output beam 58 will change so that there is now destructive interference in the etalon 30 and the beam 62 will be "off".
  • the beam is turned “on” and “off” by the signal source 72 applying the appropriate forward current I_ or I D , respectively, to the diode 56.
  • the timing of the signals applied to the diode is related to the angular position of the disc (being driven in rotation by the motor 54) which controls the -Im ⁇ position of the point of incidence of the beam in its scan line along the photosensitive web 70 on the drum 68.
  • Fig. 2 shows the lengths and slopes of the drift regions 28 as being substantially equal and the heights of the jumps 26 as being substantially equal. This condition might not be found in reality and the lengths of some drift regions will be longer than others. Indeed each laser diode, even of the same batch of the same model, will have its own characteristics in this respect. Thus, it will probably be advantageous to analyze each diode and select that drift region which has the most advantageous combination of length and slope. The selected drift region becomes the drift region in which the diode is operated. Overriding the selection of the drift region is that the frequency of the output beam be acceptable to the system in which the diode is employed.
  • the frequency change needed to cause a change in the beam from "on” to “off” in a modulator in accordance with the invention need be only of the order of a hundredth of the frequency change which occurs when the current in a laser diode is varied sufficiently to cause the beam output by the diode to go from "on” to "off".
  • the displacement of the "spot" where the beam is incident on the photosensitive web, transversely of the scan line and due to the frequency change in the diffractive system may be so small as to be unnoticeable, whereas in a system lacking the interferometer, displacement would be intolerable.
  • Such other embodiments might have a reflectance value R for the reflective coatings of the etalon, of R - 0.3 which, as can be seen in Fig. 4, gives an almost sinusoidally varying normalized intensity, i.e. low finesse. .
  • a particular etalon does not have the desired pathlength with the near normal angle of incidence described above, or that it is desired for some other reason to vary the pathlength in the etalon.
  • Such variation may be achieved by rotating the etalon about an axis parallel to the planes of the surfaces on which are the reflective coatings. This rotation effectively changes the angle of incidence of the light beam on the etalon. If the angle of incidence is changed, the angle of the beam within the transmissive plate 32 is also changed. Change in the angle of the beam within the plate causes change in the pathlength within the plate.
  • temperature stabilizing means may be provided for the diode.
  • temperature stabilizing means it is used in the selection of the particular frequency drift region 28 in which the diode is operated.
  • the temperature of the diode is adjusted until, at a particular selected forward current, the frequency of the output beam and the frequency at the middle of the drift region selected for the diode to operate in, are the same.
  • both the current and the temperature of the diode may be adjusted to arrive at an operating condition in the middle of a selected drift region 28.
  • a writing scanner as diagrammatically represented in Fig. 5 was designed having the following characteristics and performance parameters: 4 Megapixels/second bandwidth(2 Mhz squarewave)
  • the laser 56 used was a Hitachi HLP-1400 laser diode with a wavelength of 830 nm and an output power of approximately 10 milliwatts.
  • the thermoelectric cooler 74 and controller 76 are stock items available from Midland Ross.
  • the signal source 72 was a Wavetek Model 166 Pulse/Function Generator. Any suitable microscope objective can be used for the collimating lens 60.
  • the etalon 30 is obtained from Laser Optics and is 3 mm thick with 97% reflectance coatings 36 on each surface.
  • the finesse is 103, having a passband width of 334 MHz and a passband separation of 34.5 GHz,
  • Grating pitch 1697 lines/mm
  • Number of facets 8 Scan angle of beam - + 16° Linear gratings perpendicular to radius at center of sector (i.e., "tangential")
  • Substrate glass
  • Incidence angle diffraction angle ⁇ 45°
  • the hologon disc 50 is attached to a motor 54 having a suitable controller 55 for maintaining motor speed. The speed required is 990 rpm.
  • the collimated scanning beam 64 from the hologon is focused to the film plane by the F ⁇ lens 66.
  • the lens not only focuses the beam but also provides a flat field focal plane and compensates for distortion, such that the spot motion is directly proportional to the hologon rotation angle.
  • the lens parameters desired are:
  • the hologon scanner provides the high speed horizontal scan.
  • the slower speed vertical scan is accomplished by rotating the drum 68.
  • the photosensitive material 70 is photographic film, Kodak SO-156.
  • the surface speed needed " at ' the drum is 0.073 inches/second.
  • the information from the signal source 72 must be synchronized to the start-of-line and start-of-page signals provided by the appropriate detectors. These functions are not shown in Figure 5 but are well known in the art.
  • the operating point of the etalon 30 initially can be set on the side of a passband by mechanically tilting the etalon and then fine tuning by adjusting the laser bias current. Operation in environments where the temperature is not well controlled may cause the operating point to drift off the side of the peak. A servo control mechanism can be added to track the drift.
  • One technique is to control the etalon temperature with a thermoelectric cooler. The device 80 and control device 82 might be used for this purpose (see Fig. 5).
  • An alternative approach is to pick off a portion of the beam after the etalon with a beamsplitter and detect it with a photodiode. An error signal derived from the photodiode signal is used to modify the laser bias to keep the laser operating on the middle of the slope of the etalon passband.
  • the term "light” has been used herein in relation to the energy emitted by the source, namely, the laser diode in the described embodiment. It is to be understood that the term is to be construed broadly as extending beyond the visible portions of the electromagnetic spectrum. Further, while the light source specifically described, namely a laser diode, emits coherent light, it is to be understood that in other embodiments of the invention the light does not have to be perfectly coherent. Light which includes a degree of coherence such that there is a useful change in interference may be used in embodiments of the present invention and the clause "at least a degree of coherence" is intended to embrace all such useful conditions.
  • a light source other than a laser diode and of light which has a degree of coherence
  • a light source consisting of a tungsten filament heated by electrical energy.
  • Light output from the heated filament is passed through a filter which passes substantially monochromatic light.
  • the monochromatic light is focussed on a pinhole.
  • Light passing through the pinhole is directed onto an interferometer, as described above.
  • collimating means are provided to collimate the divergent beam emitted by the laser diode, it is to be understood that if the laser diode emits a collimated beam, collimating means need not be provided. At present, it is believed that there does not exist a laser diode which emits a collimated beam, but that progress is being made towards such a laser diode. Thus, such a diode would constitute means for producing a collimated light beam whereas at present such means might comprise a laser diode emitting a divergent beam and collimating means for collimating the divergent beam into a collimated beam.
  • the etalon may include two transmissive plates maintained in parallel spaced relationship by low thermal expansion material. The plates have reflective transmissive coatings on their facing surfaces.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Nonlinear Science (AREA)
  • Condensed Matter Physics & Semiconductors (AREA)
  • Electromagnetism (AREA)
  • Semiconductor Lasers (AREA)

Abstract

Un générateur de lumière modulable (56, 60, 30) comprend une iode à laser (56) dont la fréquence d'émission varie en fonction du courant qui la traverse. Une alimentation électrique variable (72) destinée à la diode à laser (56) commande le changement de fréquence du faisceau de sortie (58, 62) de la diode (56). Le faisceau de sortie (58, 62) est incident sur un interféromètre de Fabry et Pérot (30), de façon à convertir la modulation de fréquence du faisceau en une modulation d'amplitude.
PCT/US1988/001450 1987-05-04 1988-05-03 Ameliorations apportees a la modulation d'un faisceau lumineux WO1988008997A1 (fr)

Applications Claiming Priority (2)

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US4549887A 1987-05-04 1987-05-04
US045,498 1987-05-04

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PCT/US1988/001451 WO1988008998A1 (fr) 1987-05-04 1988-05-03 Ameliorations apportees a la modulation d'un faisceau lumineux

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2512298A1 (fr) * 1981-09-03 1983-03-04 Int Standard Electric Corp Systeme et methode de modulation de frequence optique
GB2161925A (en) * 1984-07-20 1986-01-22 Stc Plc Fibre optic sensor
WO1986001006A1 (fr) * 1984-07-30 1986-02-13 American Telephone & Telegraph Company Source de lumiere modulee en intensite a haute vitesse

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2512298A1 (fr) * 1981-09-03 1983-03-04 Int Standard Electric Corp Systeme et methode de modulation de frequence optique
GB2161925A (en) * 1984-07-20 1986-01-22 Stc Plc Fibre optic sensor
WO1986001006A1 (fr) * 1984-07-30 1986-02-13 American Telephone & Telegraph Company Source de lumiere modulee en intensite a haute vitesse

Non-Patent Citations (3)

* Cited by examiner, † Cited by third party
Title
Applied Optics, volume 26, no. 1, 1 January 1987, Optical Society of America, (New York, US), Kimio Tatsuno et al.: "Diode laser direct modulation heterodyne inter-ferometer", pages 37-46 *
Optical Engineering, volume 20, no. 6, November-December 1981, Society of Photo-Optical Instrumentation Engineers, (Bellingham, Washington, US), P.D Atherton et al.: "Tunable Fabry-Perot filters", pages 806-814 *
Optics and Spectroscopy, volume 17, no. 1, July 1964, (Washington, DC, US), N.B. Kravtsov et al.: "On the possibility of converting phase and frequency modulation of light into amplitude modulation", page 74 *

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