WO1998028736A1

WO1998028736A1 - Optical system having an increased angular scan range

Info

Publication number: WO1998028736A1
Application number: PCT/IB1997/001520
Authority: WO
Inventors: Johannes Schleipen; Graham Thomason
Original assignee: Koninklijke Philips Electronics N.V.; Philips Norden Ab
Priority date: 1996-12-24
Filing date: 1997-12-04
Publication date: 1998-07-02
Also published as: EP0891620A1; CN1216140A; JP2000507004A

Abstract

The invention relates to an optical system (1) comprising a radiation source (3) for supplying a radiation beam, and means for providing the radiation beam with a scanning movement through an angular range ΔΥ. The light path of the scanning radiation beam incorporates at least one set of two optical interfaces (9, 11). The two interfaces (9, 11) mutually enclose an angle α and enclose a material having a refractive index n which is different from that of its surroundings.

Description

Optical system having an increased angular scan range.

The invention relates to an optical system comprising a radiation source for supplying a radiation beam, and means for providing the radiation beam with a scanning movement through an angular range Δθ.

The invention also relates to an apparatus for scanning an information plane, particularly an optical tape recorder, and a bar code scanner.

An optical system of the type described in the opening paragraph is known from, for example, United States Patent US-A 5,333,144. This Patent describes a number of embodiments of an optical system generating a radiation beam which makes a scanning movement within a given angular range. The magnitude of the angular range is determined by the wavelength range within which the laser can generate radiation. In this system, the scanning movement is realized in an optical manner.

However, in apparatuses using one of the optical systems, described in said US Patent, for generating a scanning beam such as, for example, a bar. code scanner or a laser-addressed display panel, an angular range which is larger than can be realized with the known systems is often desired.

It is an object of the present invention to provide an optical system with which a scanning beam having an increased scan range can be realized without complicating the optical system.

To this end, the optical system according to the invention is characterized in that the light path of the scanning radiation beam incorporates at least one set of two optical interfaces mutually enclosing an angle a and enclosing a material having a refractive index n which is different from that of its surroundings. An optical interface is understood to mean a transition from an optically dense to an optically less dense medium, or conversely. Generally, the optical system will be present in air, so that n > 1.

The invention is based on the recognition that the scan range Δθ of a scanning beam can be increased by making use of the refraction of the radiation beam on two non-parallel optical interfaces.

When a radiation beam is incident on an optical interface, there will be refraction. This refraction is generally described by Snellius' law: n_j . sin (θ_j) = n₀ . sin (ΘJ in which n_j and n₀ are the refractive indices of the medium emitting the radiation beam and the medium receiving the radiation beam, respectively, θ_j and θ₀ are the angles of incidence with respect to the normal on the interface and the exit angle with respect to this normal, respectively.

In the case of two interfaces, θ^, is considered to be the angle of incidence on the first interface and θ_out is considered to be the exit angle on the second interface.

On the first interface, there will apply: sin (θ_in) = n . sin (θ_m) in which n is the refractive index of the medium between the two interfaces and ^ is assumed to be 1. θ_m is the exit angle with respect to the normal on the first interface.

On the second interface, there will apply: n . sin ( - θ_m) = sin (θ_out) if the angle enclosed between the two interfaces is α. a - θ_m is now the angle of incidence measured with respect to the normal on the second interface. It follows that θ_out = arc sin [n . sin (a - θ_m)]

In this way, the angular range Δθ of the optical system can be considerably increased for a given incidence angular range.

It is to be noted that there is a maximum value of the angle of incidence on the interfaces, referred to as the critical angle θ_g, for a transition from an optically dense to an optically less dense medium. Below this maximum value, an incident beam will undergo total internal reflection on the interface instead of being refracted. The increase of the angular range is maximal when θ_m is approximately equal to θ .

An embodiment of the optical system according to the invention is characterized in that the light path of the scanning radiation beam incorporates a first set and a second set of two optical interfaces, the interfaces of the first set enclosing an angle <x_j and the interfaces of the second set enclosing an angle ₂, the sets mutually enclosing an angle β. The angular scan range is thereby even further increased. This has the further advantage that, notably when the angular scan is realized by means of wavelength modulation of a diode laser in combination with a grating, the non-linearity of the angular scan realized by diffraction on the grating is considerably reduced so that the increased angular scan is substantially linear.

Another embodiment of the optical system according to the invention is characterized in that the system comprises one set of optical interfaces and a plurality of reflective surfaces which ensure that the scanning light beam passes each interface twice.

In this way, a single set of interfaces is sufficient. However, each interface is passed twice so that the same effect is achieved as with four interfaces, but the light path is folded, which contributes to the compactness of the system.

Yet another embodiment of the optical system according to the invention, having the same advantage, is characterized in that the system comprises two sets of optical interfaces, in which the sets have one interface in common, and in that the system further comprises a plurality of reflective surfaces which ensure that the scanning beam passes the common interface twice and the other interfaces once.

A further embodiment of the optical system according to the invention is characterized in that the optical interfaces of a set form part of a prism having an aperture angle which is equal to the angle enclosed by the two interfaces.

Such an element is a simple optical element. The refractive index of the material of the prism is then n.

Another embodiment of the optical system according to the invention is characterized in that the optical interfaces are constituted by the walls of a wedge-shaped liquid crystalline cell.

Liquid crystalline material generally also has a suitable refractive index to achieve the desired effect. An electric field may be applied across the liquid crystalline cell, with the result that the angular scan can be manipulated electrically. There are different possibilities of realizing a scanning beam.

An embodiment of the optical system according to the invention is characterized in that the means comprise a wavelength-selective feedback element with which the wavelength of the radiation beam from the diode laser is variable by means of feedback to the diode laser, and in that the means further comprise a dispersive element for wavelength-dependent refraction of the radiation beam to be generated by the diode laser.

By feeding back the desired wavelength to a diode laser at the suitable instant, the diode laser will be forced to emit radiation having this wavelength. The wavelength of the diode laser can be varied by ensuring that the fed-back wavelength changes. This may be realized by placing an adjustable wavelength-selective feedback element in the radiation beam of the diode laser. In this way, a wavelength modulation of the diode laser is obtained. By placing a dispersive element, for example a grating, in the wavelength-modulated beam, the wavelength modulation is subsequently converted into an angular scan. Reference is made to United States Patent US-A 5,333,144 on the possibilities of using the adjustable wavelength-selective feedback element and its description.

Another embodiment of the optical system according to the invention is characterized in that, viewed from the diode laser, the means comprise a first grating, a second grating and a feedback element, the feedback element being divided into a plurality of discrete areas, at least one of which is reflective.

The first grating splits the beam emitted by the radiation source into spectral components which are rendered parallel by the second grating before they are incident on the feedback element. The feedback element will be reflective at least in a given area, which means that, due to the dispersion, only the beam having the wavelength incident on the reflecting area will be fed back to the radiation source. Said feedback element may be, for example a mask or an optical disc or an array of liquid crystals.

Another embodiment of the optical system according to the invention is characterized in that the means comprise a rotatable scanning element in the form of a polygon mirror. The beam supplied by the radiation source is incident on a rotating polygon mirror, so that a scanning beam is realized in a mechanical way. The wavelength of the radiation beam emitted by the radiation source does not play a role in this case.

The invention also relates to a plurality of optical apparatuses in which the optical system according to the invention can be used to great advantage. These and other aspects of the invention are apparent from and will be elucidated with reference to the embodiments described hereinafter.

In the drawings:

Fig. 1 shows an embodiment of an optical system according to the invention, with one set of two optical interfaces;

Fig. 2 shows an embodiment of an optical system according to the invention, with two sets of two optical interfaces;

Fig. 3 shows an embodiment of a wedge-shaped liquid crystalline cell; Figs. 4(a), 4(b) and 4(c) show some embodiments of an optical element with which the same increase of the scan range can be realized as with two sets of two interfaces;

Fig. 5 shows an embodiment of an optical system with which a scanning beam can be generated and in which the present invention can be used; Figs. 6(a) and 6(b) show some graphs in which θ_out is shown as a function of θ^ for a system with one set of interfaces enclosing angle of 45° for two different values of n, showing also the critical angle θ_g;

Figs. 7(a) and 7(b) show graphs in which θ_out is shown as a function of θ_m for a system with one set of two optical interfaces enclosing an angle of 45° for two different values of β;

Figs. 8(a) to 8(b)) show some graphs in which θ_out is shown as a function of θ_ώ for a system with two sets of optical interfaces each enclosing an angle of 30° for two different values of β;

Fig. 9 shows an embodiment of an optical system with a rotating polygon mirror;

Fig. 10 shows an embodiment of a laser printer which may be provided with an optical system according to the invention;

Fig. 11 shows an embodiment of an image display apparatus which may be provided with an optical system according to the invention; Fig. 12 shows an embodiment of a radiation-addressable display panel, and

Fig. 13 shows an optical apparatus for reading a one-dimensional or multidimensional bar code, provided with an optical system according to the invention.

Fig. 1 shows diagrammatically an embodiment of an optical system 1 supplying a scanning radiation beam having an angular range of Δθ. The radiation source 3 may be, for example a diode laser whose radiation is incident on an adjustable wavelength- selective feedback element 5. Adjustable is herein understood to mean that the wavelength fed back from the spectrum of the diode laser is variable. The feedback element 5 may be, for example an optical waveguide having an integrated grating with a varying period, a reflective element having a variable reflection, an electro-optical element or an acousto- optical element. The feedback element may be, for example partially transmissive. For the detailed description of systems supplying a scanning beam with one of the above-mentioned feedback elements, reference is made to United States Patent US-A 5,333,144. The wavelength of the light fed back to the diode laser 3 is thus determined by adjusting the feedback element. As a result of this feedback, the diode will generate radiation with the fed-back wavelength. By varying the adjustment of the feedback element, the fed-back wavelength, and hence the wavelength emitted by the diode laser, can be varied. A grating 7 is arranged behind the feedback element. Different wavelengths are diffracted at different angles by means of the grating 7. In this way, a scanning beam can be generated by means of a wavelength-variable diode laser. In fact, the wavelength modulation of the diode laser is converted into an angular scan.

In the optical system according to the invention, at least two optical interfaces 9, 11 are arranged in the light path of the scanning beam, which interfaces mutually enclose an angle and enclose a material having a refractive index n which is different from the refractive index of the surrounding medium. Optical interface is herein understood to mean a transition from an optically dense to an optically less dense medium, or conversely. Generally, this optical system will be present in air, so that n > 1. In this way, it is possible to realize an angular scan through a larger angular range. This result can be explained with reference to Snellius' law: n_j . sin (θ_j) = n₀ . sin (Θ_Q) in which n_j and n₀ are the refractive indices of the medium emitting the radiation beam and the medium receiving the radiation beam, respectively. θ_; and θ₀ are the angle of incidence with respect to the normal on the interface and the exit angle with respect to this normal, respectively.

When the angle of incidence on the first interface 9 with respect to the normal 13 on this interface 9 is referred to as θ_in and the exit angle on the second interface 11 with respect to the normal 15 on this interface 11 is referred to as θ_out, there will apply, on the first interface: sin (θ_in) = n . sin (θ_m) in which n is the refractive index of the medium between the two interfaces and ^ is assumed to be 1. θ_m is the exit angle with respect to the normal on the first interface. There will apply, on the second interface 11: n . sin ( - θ_m) = sin (θ_out) if the angle enclosed between the two interfaces is a. a - θ_m is now the angle of incidence measured with respect to the normal 15 on the second interface.

By incorporating at least a set of two non-parallel interfaces enclosing a medium having a refractive index n which is different from the refractive index of the ambience in the light path of a scanning beam, the angular range of the scanning beam can be increased considerably.

Fig. 1 shows an embodiment in which the two optical interfaces form part of a prism having an aperture angle . The interfaces 9, 11 may also be constituted by the walls of a wedge-shaped liquid crystalline cell having an aperture angle a. The cell may also be switchable so that it is achieved that n _C and, consequently, the scanning angle can be varied.

A wedge-shaped liquid crystalline cell is known per se from, for example United States Patent US-A 4,958,914. Fig. 2 shows an embodiment of an optical system in which two prisms are placed one behind the other. Thus, there are four optical interfaces (9, 11) and (17, 19) in this embodiment. The interfaces enclose an angle a_x in the first set (9, 11) and an angle α₂ in the second set (17, 19). The two sets mutually enclose an angle β. By making use of two sets of interfaces, the angular range is even further increased and the scanning symmetry is optimized. Moreover, if the scanning beam is realized by a wavelength modulation which is converted into an angular scan by means of a grating, the angular scan will not be linear due to diffraction on the grating. By making use of two sets of two non-parallel interfaces, this non-linearity can be reduced considerably.

Two prisms or two wedge-shaped liquid crystalline cells, or a combination of a prism and a cell may of course be used for the two sets of interfaces.

Fig. 3 shows an embodiment of a wedge-shaped liquid crystalline cell 41. The liquid crystalline material 43 is present between two optically transparent plates 45, 47 and has a refractive index n_LC.

Another embodiment with which an increase of the angular range of a comparable magnitude can be realized is to use only two non-parallel interfaces 21, 23 in combination with three reflective surfaces 25, 27, 29, as is shown in the embodiments of Figs. 4(a) and 4(b). The beam passes each interface 21, 23 twice, so that the result corresponds to that of four interfaces. In Fig. 4(c), only two reflective surfaces 25, 27 are required, but the third side face of the prism or the side wall of a wedge-shaped cell is used as an optical interface 31. Here, two sets of two interfaces are actually used, with the two sets having a common interface.

Together with the interfaces, the surfaces may constitute an optical tunnel so that substantially no light is lost. An advantage of these embodiments if that the light path is folded and that the optical system can therefore be given a more compact form. Fig. 5 shows another embodiment of an optical system with which a scanning beam can be made and in which the invention may be used to great advantage. The radiation beam b supplied by the diode laser 3 is incident on a first grating 35 via a collimating lens 33. The different wavelengths in the beam are spatially separated on this grating into sub-beams b_j, b₂, b₃. These beams are subsequently incident on a second grating 37, on which each wavelength is deflected at a different angle, such that a parallel beam b' is obtained. This parallel beam b' is incident on a feedback element 39 which is divided into a number of discrete areas 51, at least one of which is reflective. Only the wavelength which is incident on an active reflective area will be fed back to the diode laser. The diode laser will be forced by this feedback to generate light having this wavelength. By varying the position of the active reflective area, a scanning beam can be realized. The scanning beam may be coupled out on the second grating 37. This may be realized in transmission in zero-order for grating 37 for in the first order for grating 35 if grating 37 is, for example 50% reflective and 50% transmissive. The beam may also be coupled out in reflection, but then, for example for the zero order of grating 37. The set or sets of interfaces are subsequently provided in the scanning beam supplied by the system shown in Fig. 5.

In an optical system according to the invention, having a set of interfaces in which the angle α is 45° and the refractive index of the enclosed medium n is 1.53, an exit angle variation of 10° may be increased to an exit angle variation of 24°. Figs. 6(a) and 6(b) each show a graph in which θ_out as a function of θ_ώ is given for two different refractive indices of the material enclosed between two optical interfaces. The angle enclosed between the interfaces is 45°. The critical angle θ. is also shown in the Figures.

Figs. 7(a) and 7(b) show some graphs in which the exit angle of an optical system according to the invention is shown as a function of the entrance angle for two different values of the angle β for a_γ = α₂ ⁼ 45°. This is an optical system with four optical interfaces.

Figs. 8(a) and 8(b) show some graphs for two different values of the angle β, now for αi = α₂ = 30°. In the optical system shown in Fig. 9, a scanning beam is generated mechanically. To this end, the system comprises a radiation source-detection unit 71 which supplies a scanning beam b, and a rotating mirror polygon 73 which reflects the, for example parallel, beam to an objective lens 75 which is capable of focusing the beam to a radiation spot. The mirror polygon comprises, for example ten mirror facets fj - f₁₀ which are, for example parallel to the axis of rotation of the mirror polygon. During operation, this polygon rotates in the direction indicated by the arrow 77. Each facet rotating in the radiation path of the beam, facet f₂ in the Figure, will move the beam in the direction indicated by the arrow 79 through the entrance pupil of the objective lens. An optical system as described here is used, inter alia, in optical apparatuses for scanning tape-shaped record carriers.

The optical system according to the invention may be used to great advantage in a number of optical apparatuses.

Fig. 10 shows the principle of a laser printer 81. In such a printer, a photosensitive layer is first written by means of a scanning laser beam. Subsequently, this layer is moved through an ink bath and then a print is made on paper. The photosensitive layer 93 may be wrapped around a roll 95 which is rotated about a shaft 97 for describing consecutive lines. The line scanning can be realized by means of, for example, a mirror polygon 99 having, for example six mirror facets f and rotating about a shaft 101, or a grating. The reference numeral 103 denotes an objective lens, for example a lens which focuses the radiation emitted by a radiation source 105, for example a high-power diode laser, and reflected by the mirror facets to a radiation spot V on the medium 93. The intensity of the laser beam is modulated in conformity with the information to be written, by modulating the current through the diode laser or by means of a separate, for example acousto-optical or electro-optical modulator 107. To detect the position of the mirror polygon in six degrees of freedom, the apparatus is provided with a position-detection system 109. Here again, two or four interfaces may be arranged between the element, which causes the beam to scan, and the radiation-sensitive layer in order to increase the scan range of the scanning beam.

Fig. 11 shows the circuit diagram of an image display apparatus 111 in which the image is generated by a reflective radiation-sensitive, i.e. radiation-addressable display panel 113. The advantage of such a panel in an image projection apparatus is described in European Patent Application EP 0 517 517. As compared with a conventional active matrix panel, the advantage of a radiation-addressable panel is that it yields a high light efficiency because it is not necessary to provide the panel surface with a matrix of electronic switches and conducting electrodes and because this panel absorbs virtually no radiation.

Fig. 12 shows the structure of the radiation-addressable panel 113. Viewed from the side of the write beam 115, it comprises a first optically transparent substrate 117, a transparent electrically conducting layer 119, for example of indium tin oxide (TTO), a photoconducting layer 121 having a high resistance in a dark ambience and a satisfactory conductance when exposed and consisting of, for example silicon, possibly a light-obstructing layer 123, a light-reflecting layer 125, for example consisting of a packet of dielectric layers having a thickness of a quarter wavelength, a first orientation layer 127, a layer of liquid crystalline material 129, a second orientation layer 131, a second transparent electrically conducting layer 133 and a second transparent substrate 135.

This panel is line-sequentially scanned by a write beam 137 emitted by a unit 139 comprising a radiation source, for example a laser, and a beam-shaping optical system, and to which the information to be displayed, for example a video signal, is applied so that the laser beam is intensity-modulated in conformity with this information. The laser beam 137 is incident on a rapidly rotating mirror polygon 141 and subsequently on a second scanning element 143 moving at a slower rate and constituted by, for example a vibrating flat mirror or by a second mirror polygon. The scanning element 143 reflects the beam towards the panel 113. The mirror polygon 141 reflects the converging beam 137 in such a way that the radiation spot formed on the photosensitive layer of the panel describes a line. The second scanning element 143 ensures a relatively slow movement of this radiation spot in a second direction perpendicular to the line direction. The photosensitive layer 113 of the panel is thus scanned in two dimensions, and a two-dimensional matrix of pixels is written. The use of a mirror polygon for scanning a display panel by means of a write beam is known from the English-language abstract of Japanese Patent Application 62-56931. A grating instead of a mirror polygon may be used as a scanning element. As described above, the scan range of the beam can be further increased by arranging two or four optical interfaces behind the scanning element 143.

The electrodes 119 and 133 are connected to a voltage source 145. As long as the photoconducting layer is dark, the electrode 119 is isolated from the liquid crystalline layer. The layer becomes conducting at each position of the photoconducting layer on which the beam 137 switched at the high intensity level is consecutively incident, and an electric field is produced locally across the liquid crystalline layer so that the orientation of the molecules in this layer changes locally and the state of polarization of a corresponding part of a read or projection beam 147 incident from the left also changes. This change of polarization is converted in known manner by means of a polarization analyzer into a variation of the intensity of the beam 149 reflected by the panel.

As is shown in Fig. 11, the panel 113 with the addressing system may be used in an image projection apparatus. This apparatus is provided with an illumination unit comprising a radiation source 151 and a beam-shaping optical system 153, which unit supplies an illumination beam. This beam illuminates the panel 113 via a polarization- sensitive beam splitter 155. The image formed in this panel is imaged on a projection screen 159 by the beam reflected by the panel and by a projection lens 157. The addressable panel with the addressing system may be alternatively used in a direct-vision apparatus, with a viewer directly watching the panel.

A position detection system 161 may be used for determining the movements of the mirror polygon 141 in six degrees of freedom.

A scanning device comprising a scanning element having an increased scan range may further be used in an image display system known as laser TV with which an image is directly written on a projection screen or on a wall functioning as such by means of a scanning laser beam, or three laser beams in the case of a color image. A laser TV apparatus is described in, for example European Patent Application 0 374 857.

The invention may also be used in scanning cameras, notably infrared cameras in which an image of a scene or object formed by an objective lens is moved across a detector or a row of detectors. Such a camera is described in, for example United States Patent US-A 3,706,484. A scanning element, for example a rapidly rotating mirror polygon or a grating, is used for line-sequentially moving the image across the detector. The invention may be used again to realize a larger scan range. Both mechanical and non-mechanical scanning devices as described above may also be used in apparatuses for inspecting objects or workpieces during or after their manufacture, or for reading codes, for example bar codes on objects, so that the invention may also be used in these devices.

Fig. 13 shows an embodiment of an apparatus for reading a one- dimensional or multidimensional bar code. Examples of such codes are a one-dimensional bar code and a two-dimensional dot code. The beam b supplied by a diode laser 161 is incident via a lens 163 on a mirror 165. A magnet 167 which, in combination with a coil 169 driven by a current source 171 causes the mirror 165 to perform a vibrating movement, is arranged at the rear side of the mirror 165. The scanning beam generated in this way is subsequently incident on a bar code 173. An optical system according to the invention, comprising one or two sets of two non-parallel interfaces, is arranged between the mirror 165 and the bar code 173. The Figure shows only one set of interfaces (9, 11).

Claims

CLAIMS:

1. An optical system comprising a radiation source for supplying a radiation beam, and means for providing the radiation beam with a scanning movement through an angular range Δθ, characterized in that the light path of the scanning radiation beam incorporates at least one set of two optical interfaces mutually enclosing an angle a and enclosing a material having a refractive index n which is different from that of its surroundings.

2. An optical system as claimed in Claim 1, characterized in that the light path of the scanning radiation beam incorporates a first set and a second set of two optical interfaces, the interfaces of the first set enclosing an angle and the interfaces of the second set enclosing an angle α₂, the sets mutually enclosing an angle β.

3. An optical system as claimed in Claim 1, characterized in that the system comprises one set of optical interfaces and a plurality of reflective surfaces which ensure that the scanning light beam passes each interface twice.

4. An optical system as claimed in Claim 1 , characterized in that the system comprises two sets of optical interfaces, in which the sets have one interface in common, and in that the system further comprises a plurality of reflective surfaces which ensure that the scanning beam passes the common interface twice and the other interfaces once.

5. An optical system as claimed in Claim 1, 2, 3 or 4, characterized in that the optical interfaces of a set form part of a prism having an aperture angle which is equal to the angle enclosed by the two interfaces.

6. An optical system as claimed in Claim 1, 2, 3 or 4, characterized in that the optical interfaces are constituted by the walls of a wedge-shaped liquid crystalline cell.

7. An optical system as claimed in any one of the preceding Claims, in which the radiation source is a diode laser, characterized in that the means comprise a wavelength-selective feedback element with which the wavelength of the radiation beam from the diode laser is variable by means of feedback to the diode laser, and in that the means further comprise a dispersive element for wavelength-dependent refraction of the radiation beam to be generated by the diode laser.

8. An optical system as claimed in any one of Claims 1 to 6, in which the radiation source is a diode laser, characterized in that, viewed from the diode laser, the means comprise a first grating, a second grating and a feedback element, the feedback element being divided into a plurality of discrete areas, at least one of which is reflective.

9. An optical system as claimed in any one of Claims 1 to 6, characterized in that the means comprise a rotatable scanning element in the form of a polygon mirror.

10. An optical apparatus for electromagnetically scanning a medium in at least one direction, characterized in that the apparatus is provided with an optical system as claimed in any one of the preceding Claims.

11. An optical apparatus for writing signs in a radiation-sensitive layer in accordance with a line pattern and being provided with a radiation source for supplying a write beam and means for modulating said beam in conformity with the information to be written, characterized in that the apparatus is provided with an optical system as claimed in any one of Claims 1 to 9.

12. An optical apparatus for electromagnetically writing a reflective display panel provided with a photoconducting layer, characterized in that the apparatus is provided with an optical system as claimed in any one of Claims 1 to 9.

13. An optical apparatus for writing an image in the form of a line pattern on a projection screen or on a surface functioning as such, characterized in that the apparatus is provided with an optical system as claimed in any one of Claims 1 to 9.

14. An optical apparatus for converting an image into an electric signal, in which the medium is a radiation-sensitive detector, characterized in that the apparatus is provided with an optical system as claimed in any one of Claims 1 to 9.

15. An optical apparatus for reading a one-dimensional or multidimensional bar code, characterized in that the apparatus is provided with an optical system as claimed in any one of Claims 1 to 9.