HK1083650B - Method and apparatus for fabricating a light management substrates - Google Patents

Description

Method and apparatus for making light management substrates

Technical Field

The present invention relates to methods and apparatus for fabricating light management (light management) films, and in particular, to such films fabricated from random or quasi-random controlled surfaces (master surfaces).

Background

In backlit computer displays or other systems, films are often used to direct or scatter light. For example, in backlit displays, brightness enhancement films use prismatic or textured surfaces to direct light along a viewing axis (i.e., perpendicular to the display), which increases the brightness of the light as viewed by a user of the display and enables the system to use less power to produce a desired level of on-axis luminous flux. Films for deflecting light may also be used in a wide variety of other optical designs, such as for projection displays, traffic signals, and illuminated signs. Backlit displays and other systems use multilayer films that are stacked and arranged such that their prismatic or textured surfaces are perpendicular to each other and sandwiched between other optical films known as diffusers. Diffusers have highly uneven or random surfaces.

Textured surfaces have been widely used in optical applications such as backlit display films, diffusers, and back reflectors. In many optical designs, microstructures must be used to redirect and redistribute light (or scattered light) to increase brightness, enhance scattering, or enhance absorption. For example, in a backlight display system, it is often necessary to both direct the light flux incident on the screen toward a direction perpendicular to the screen and spread the light flux over the entire viewing space. The performance of thin film solar cells can be significantly improved by light trapping and angle selective specular reflectors based on textured TCO/glass/metal substrates. The microstructure is sometimes randomized to reduce the creation of defects such as pits and defects originating from the optical interface between two elements, such as moire, speckle, and newton's rings. Ideally, instead of two or more films together, one optical film should have both brightness enhancing properties and minimal defects.

In backlight applications, brightness enhancement films and diffuser films are often incorporated as part of the display screen for redirecting and redistributing light. In the prior art, a typical solution to increase brightness is to use an optical film having a surface structured with linear prisms. For example, the prior art describes the use of prismatic films to increase on-axis brightness of backlit liquid crystal displays. To avoid manufacturing defects and reduce optical coupling, optical films having structures with randomly varying heights along their length have been designed to achieve brightness enhancement while avoiding manufacturing defects and reducing optical coupling between two sheets of such films.

Disclosure of Invention

A method for processing the surface of a workpiece is realized by the following steps: contacting a cutting tool (110) with a surface of a workpiece; and for at least one cutting pass i, causing relative motion between the cutting tool (110) and the surface of the workpiece along a path on the surface of the workpiece. The path is essentially a mathematical function defined over an interval C of a coordinate system, characterized by a set of non-random, random or quasi-random parameters selected from amplitude, phase and period or frequency.

The relative movement between the cutting tool and the surface of the workpiece is achieved by: band-pass filtering a noise signal (104); providing the band-pass filtered noise signal to a function generator (106); generating a randomly modulated mathematical function by a function generator; relative motion between the cutting tool (110) and the surface of the workpiece is directed along a path on the surface of the workpiece in response to the function of the random modulation.

The present invention functions by modulating the prism structure of the optical film in the transverse direction (the direction perpendicular to the height) from a nominally linear path using non-random, random (or quasi-random) amplitudes and periods. A master tool for a tool to make a film having such a microstructure can be made by diamond turning on a cylindrical drum or flat plate. The drum is typically coated with hard copper or nickel on which grooves are cut in a thread or ring shape. The drum rotates while for thread cutting or ring cutting the diamond cutting tool is moved transversely to the direction of rotation to produce the desired pitch. To achieve modulation, a Fast Tool Servo (FTS) system is used to drive the tool laterally. Piezoelectric transducers are used to move a diamond tool to a desired displacement by varying the voltage applied to the transducer at random or quasi-random frequencies. The displacement (amplitude) and frequency at any time can be randomly generated in a personal computer and then sent to an amplifier to produce the desired voltage. Due to temperature and hysteresis effects of the piezoelectric material, a feedback control of the distance probe may be required to ensure proper tool movement. To modulate the cut in both the lateral and height directions, an FTS with two sum detectors with independent controllers can be used.

The present invention reduces the number of components in the optical system, thereby reducing cost and weight. In general, it improves optical performance by minimizing many possible optical interferences and couplings. The manufacturing method provides microstructures with more control over the direction of light.

The present invention achieves light enhancement and scattering without the use of optical elements by randomly varying the prism structure in the lateral and height directions. Due to the random component in the transverse direction, optical defects caused by interference between the two optical films, such as moire, speckle, and newton's ring, substantially disappear. The lateral variation is more effective than the height variation in producing scattering and reducing optical defects, especially the moire effect. The randomness of the prism pattern enables blending of the joints of the machined segments without visible seams. The length of the drum is not limited by the cutting tool travel. The lateral movement of the cutting tool has feedback control to ensure accurate positioning to overcome hysteresis, creep and temperature effects of the piezoelectric stack. The combination of lateral and elevation variations provides greater freedom to machine surface microstructures for many applications such as diffusers, solar panels, reflectors, and the like.

Drawings

FIG. 1 is a flow chart illustrating a method of machining a surface of a workpiece, wherein the workpiece is a master (master) drum;

FIG. 2 is a flow chart illustrating a method of machining a surface of a workpiece, wherein the workpiece is a master template;

FIG. 3 is a representation of the master drum of FIG. 1 having a random or quasi-random pattern thereon along a substantially helical or spiral-like path;

FIG. 4 is a representation of the master drum of FIG. 1 having a random or quasi-random pattern on substantially concentric rings;

FIG. 5 is a diagram of the master template of FIG. 2 having a random or quasi-random pattern thereon along a substantially saw-tooth or triangular path;

FIG. 6 is a diagram of the master template of FIG. 2 having a random or quasi-random pattern thereon along a series of substantially concentric rings;

FIG. 7 is a pictorial view of a cross-section of a cutting tool of a prismatic configuration in nature;

FIG. 8 is an illustration of the prismatic cutting tool of FIG. 5 having compound angle cutting faces;

FIG. 9 is a graphical representation of the magnitude of the power spectral density of the randomized surface of the workpiece as a function of spatial frequency;

FIG. 10 is a top view of a randomized surface of a workpiece resulting from the method of the invention;

FIG. 11 is a graphical representation of multiple paths resulting from multiple passes of a cut on a surface of a workpiece;

FIG. 12 is a schematic representation of a system and apparatus for processing a surface of a workpiece in communication with a remote location via a communications or data network;

FIG. 13 is a graphical representation of a mathematical function;

FIG. 14 is a three-dimensional view of a backlit display device;

FIG. 15 is a schematic representation of a master machining system with fast tool servo for cutting grooves with lateral undulations in the surface of a workpiece; and

fig. 16 is a graphical representation of the cutting gradient introduced to the surface of the work surface of the workpiece.

Detailed Description

Referring to fig. 1, a method of machining a surface of a workpiece is shown generally at 100. The noise signal 102 is filtered by a band pass filter 104 and provided as an input to a function generator 106. A modulated mathematical function, such as in the form of a sine wave, is provided as an input by the function generator 106 to a servo 108. The noise signal 102, the band pass filter 104 and the function generator 106 may be replaced by a computer system equipped with appropriate signal processing software and digital to analog conversion boards to generate the input signal to the servo 108. The servo 108 guides the relative motion between the cutting tool 110 and the surface of the drum 112, wherein the drum 112 rotates at an angular velocity ω in a cylindrical coordinate system (r, θ, z). As the drum 112 rotates at an angular velocity ω, the cutting tool 110 moves relative to the drum 112 along the drum axis z and randomly back and forth parallel to the axis of the drum 112 at a frequency up to about 2000 Hz. The cutting tool 110, which is in continuous contact with the surface of the rotating drum 110, cuts and machines a randomized helical or thread pattern 116 (fig. 3) on the surface of the drum 112 in such a way that the pattern has a pitch P. For a two-axis cutting tool 110, the cutting tool not only moves back and forth parallel to the drum axis 112, but also moves perpendicular to the drum surface to cut different depths on the surface of the drum 112.

Alternatively, as shown in fig. 2, the cutting tool 110 may be in contact with the surface of a flat plate 114 moving at a velocity v in a cartesian coordinate system (x, y, z). Similarly, as the flat plate 114 moves at a velocity v and the cutting tool 110 randomly moves back and forth across the plate, the cutting tool 110, which is in continuous contact with the surface of the flat plate 114, cuts or machines a randomized triangular pattern 122 (FIG. 5) on the surface of the flat plate 114.

In another embodiment of the present invention, as shown in FIG. 4, the drum 112 need not move along the z-axis when it rotates. Likewise, the cutting tools are along a series i on the surface of the drum 112The concentric rings 118 produce a randomized or quasi-randomized pattern whereby the cutting tool returns to the starting point 122 for each cutting pass. To achieve good cut quality, a control system may enable the cutting tool 100 to repeat any ith pass several times depending on the desired final depth of cut and feed rate. When the cutting tool 110 completes a certain number of revolutions and returns to the starting point 122 of the ith cutting pass, the cutting tool 110 translates or steps by a distance S_iTo the next or kth cutting pass.

It should be appreciated that the cutting tool 110 may have more than one axis of travel. For example, it may have three axes of travel r, θ, z in a cylindrical coordinate system and three axes of travel x, y, z in a rectangular coordinate system. Such an additional axis would, for example, enable the cutting of a toroidal (toroidal) lens-type structure using a radiused cutting tool 110, or enable a gradient along the depth of cut in the cut. The translation axes (translational axes) r, θ, z and x, y, z will also enable a cutting gradient to be introduced in the pattern machined into the surface of the workpiece 112, 114 for subsequent passes of the cut. Such a cutting gradient can best be seen with reference to fig. 16. In FIG. 16, the ith pass has a thickness or width w_iThe kth pass having a thickness w_kWherein w is_iGreater or less than w_k. In addition, the nth pass has a width w_nWherein w is_nGreater or less than w_k. It will be appreciated that the thickness variations in the cutting pattern in successive cutting passes may be non-random, random or quasi-random. Other rotational degrees of freedom (e.g., pitch 152, yaw 150, and roll 154, fig. 1, 2, 5, and 6) may be used to change the angular orientation of the cutting tool 110 relative to the surface of the workpiece 112, 114, thereby changing the geometry of the cutting surface (face) machined onto the master surface.

The randomized or quasi-randomized pattern machined onto the surface of the workpiece 112, 114 is essentially a mathematical function defined over an interval on a coordinate system characterized by a set of random or quasi-random parameters selected from amplitude, phase and frequency. For a rotating drum 112, the interval C over which the mathematical function is defined is the circumference of the drum 112. For moving plate 114, the interval over which the mathematical function is defined is the width or length of plate 114. One exemplary mathematical function is a sine wave equation 1:

y_i＝A_isin{ψ_i}+S_i (1)

wherein y is_iIs the instantaneous displacement of the cutting tool relative to C in the ith cutting pass, A_iIs the displacement of the cutting tool relative to C,. psi_iIs y_iOf (a) and S_iIs y_iTranslation of the starting position.

In equation (1), the phase ψ_iComprises the following steps:

where φ is a number between zero and 2 π radians (inclusive of zero and 2 π). In order to return the cutting tool 110 to the starting position 122 located at the end of the ith cutting pass, the interval C over which the mathematical function is defined is equal to the wavelength λ_iAn integer of one half. Thus, for the ith pass:

or

Where N is a randomly or quasi-randomly selected positive or negative integer. In the case of the equation (2),is corrected by the k-th cutting pass_iAn additional factor of phi_iIs a randomly or quasi-randomly chosen number between zero and 2 pi radians (inclusive of zero and 2 pi).

Further, in equation (1), the phase ψ_iCan be as follows:

wherein a is_iAnd b_iIs a scalar quantity and Ω i is a non-random, randomly or quasi-randomly chosen number between zero and 2 π radians (inclusive).

It should be understood that the mathematical function described above may be any mathematical function that can be programmed into a Computer Numerical Control (CNC) machine. Such functions include, for example, the well-known trigonometric, sawtooth and rectangular wave functions (fig. 13), each of which may be randomly modulated in amplitude, phase and frequency.

Referring to fig. 7 and 8, cutting tool 110 comprises a prismatic structure whose cross-section may include flat cutting faces 130, 132 intersecting at one end at a peak angle 2 θ. The prismatic shaped cutting tool 110 may also include linear sections 138, 140 of the cutting faces 132, 134, resulting in a compound-angle prism. The compound-angled prism shape has a first cutting face 138 angled at an angle alpha relative to the base of the prism shape 110 and a second cutting face 140 angled at an angle beta. As best appreciated from fig. 7 and 8, the cutting tool 110 may have a cross-section with rounded peaks 134 or radii "r". In general, the cutting tool may have a cross-section having any manufacturable shape.

The apparatus required to machine the surfaces of the workpieces 112, 114 in the present invention is shown in figure 12. Machining the surface of the workpiece 112, 114 is accomplished by implementing a method that uses a Computer Numerical Controlled (CNC) milling or cutting machine 202 having a cutting tool 110, wherein the cutting tool 110 is controlled by a software program 208 installed on a computer 204. The software program 208 is written to control the movement of the cutting tool 110. The computer 204 is interconnected to the CNC milling machine 202 by a suitable cable system 206. Computer 204 includes a storage medium 212 for storing software program 208, a processor for executing program 208, a keyboard 210 for providing manual input to the processor, and a network card for communicating with a remote computer 216 via the internet 214 or a local area network.

In fig. 15, a control machining system having a fast tool servo for cutting grooves having lateral undulations in the surface of a workpiece is shown generally at 400. The input/output data processor 402 provides a cut command to a Digital Signal Processing (DSP) unit 404, and the digital signal processing unit 404 provides a signal to a digital-to-analog (DA) converter 406. A voltage amplifier 408 receiving the signal from the DA converter 406 drives a fast tool servo 410 to direct the movement of the cutting tool 110. The cutting tool position detector 412 detects the position of the cutting tool 110 and provides a signal indicative of the cutting tool position to the sensor amplifier 418, which amplifies the signal. The amplified signal is directed to an analog-to-digital (a/D) converter 420. The lathe encoder 414 determines the position of the workpiece (e.g., drum 112) and provides a feedback signal to the a/D converter 420. The a/D converter thus provides as an output a feedback signal indicative of the position of the cutting tool 110 and the position of the workpieces 112, 114 to the digital signal processor unit 404, while the DSP unit 404 provides a processed signal to the input/output processor 402.

The method is carried out to obtain a randomly or quasi-randomly machined surface of the workpiece 112, 114. When the computer 204 with the software program 208 installed therein is in communication with the CNC milling machine 202The operator is ready to initiate the method which will randomly or quasi-randomly machine the surface of the workpiece 112, 114. Implementing the method, the operator provides the value A as input to the personal computer 204_iAnd psi_iAnd starting operation. The operator input may be entered by typing A using the keyboard 210_iAnd psi_iThe value of (c) is manually provided. The one or more mathematical functions (fig. 13) may be stored in computer memory or on a remote computer 216 and accessed via the internet 214 or via a local area network.

The operator is prompted to provide a into the CNC machine 202_iAnd psi_iThe value of (c). Once these values are provided, the cutting element 110 of the CNC machine 202 begins to mill the workpiece 112, 114. The commands provided by the software program 208 will precisely direct the cutting tool 110 to mill the workpiece 112, 114 accordingly. This is accomplished by monitoring the movement of the cutting tool 110 in an appropriate coordinate system. In addition, the program 208 precisely controls the depth to which the milling process is applied. This is also accomplished by monitoring the movement of the cutting tool 110 in a coordinate system. It is best understood that the nonrandomized, randomized, or quasi-randomized surfaces of the workpieces 112, 114 resulting from the machining process can be in the form of a "positive" or "negative" master (master).

An optical substrate 142 (FIG. 10) can be created from the master by forming a negative or positive electroform over the surface of the workpiece 112, 114. Alternatively, a mold material, such as an Ultraviolet (UV) or thermal curing epoxy material or silicon material, may be used to form a stamp (replica) of the original positive or negative master mold. Any such stamp may be used as a mold for the plastic part. Molding, injection molding or other methods may be used to form the part.

In surface metrology, the autocorrelation function R (x, y) is a measure of the randomness of a surface. However, at a certain correlation length l_cIn the above, the value of the autocorrelation function R (x, y) decreases to a fraction of its initial value. For example, 1.0The autocorrelation values are considered to be highly or fully correlated surfaces. Correlation length l_cIs the length of a certain fraction at which the value of the autocorrelation function is the starting value. Typically, the correlation length is based on 1/e or a value of about 37% of the starting value of the autocorrelation. A larger autocorrelation length means that the randomness of the surface is smaller than for a surface with a smaller autocorrelation length.

In some embodiments of the present invention, the value of the autocorrelation function of the three-dimensional surface of the optical substrate 142 drops to less than or equal to 1/e of its initial value over a correlation length of about 1cm or less. In other embodiments, the value of the autocorrelation function drops to 1/e of its initial value over a length of about 0.5cm or less. For other embodiments of the substrate, the value of the autocorrelation function along length 1 drops to less than or equal to 1/e of its starting value over a length of about 200 microns or less. For other embodiments, the value of the autocorrelation function along the width w drops to less than or equal to 1/e of its starting value over a length of about 11 microns or less.

In fig. 14, a perspective view of a backlit display 300 is shown. The backlight display device 300 comprises a light source 302 for generating light 306. The light guide 304 guides the light 306 along itself by Total Internal Reflection (TIR). The light guide 304 contains breaking structures that cause light 306 to escape the light guide 304. These fracture features can include, for example, a surface made from a master tool having a cutting gradient machined thereon as described with respect to FIG. 16. A reflective substrate 308 disposed along the lower surface of the light guide 304 reflects all light escaping from the lower surface of the light guide 304 back through the light guide 304 and toward an optical substrate 314 fabricated from a positive or negative master mold having a non-randomized, randomized or quasi-randomized surface. At least one optical substrate receives light 306 from the light guide 304. The optical substrate 314 includes a planar surface 310 on one side and a randomized surface 312 on the other side that results from the randomized surface of the workpiece 112, 113 (e.g., master drum or master template). The optical substrate 314 may also include a randomized surface on both sides thereof. The optical substrate 314 receives the light 306 and functions to deflect and scatter the light 306 in a direction substantially perpendicular to the optical substrate 314 along the direction z as shown. The light 306 is thus directed to the LCD for display. A diffuser 316 may be positioned over the optical substrate 314 to achieve diffusion of the light 306. The substrate 314 may be a retarder film that is used to rotate the plane of polarization of the light exiting the optical substrate 314 so that the light better matches the input polarization axis of the LCD. A half-wave retarder, for example, may be used to rotate the substantially linearly polarized light exiting the optical substrate 314. Retarders can be formed by stretching a textured or untextured polymeric substrate along one axis of the polymer in the plane of the substrate. Alternatively, a liquid crystal device or a solid crystal device may be used. Alternatively, the retardation film 316 may be provided to the LCD substrate on the lower side for this purpose.

Any reference to first, second, etc. or front and back, left and right, top and bottom, upper and lower, horizontal and vertical, or other words expressing one variable or quantity relative to another is, unless otherwise stated, for convenience of description and does not limit the invention or its components to any one positional or spatial orientation. The dimensions of the components in the figures may vary depending on the possible designs and the desired use of the embodiments without departing from the scope of the invention.

While the invention has been described with reference to several embodiments thereof, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.

Claims (21)

1. A method of machining a surface of a workpiece (112, 114), the method comprising:

contacting a cutting tool (110) with a surface of the workpiece (112, 114); and

for at least one cutting pass i, such that relative motion between the cutting tool (110) and the surface of the workpiece follows a path (116, 122) on the surface of the workpiece (112, 114), wherein i is an integer indicative of the number of cutting paths;

wherein the path (116, 122) is essentially a mathematical function defined over an interval C of a coordinate system, characterized by a set of non-random, random or quasi-random parameters selected from the group consisting of amplitude, phase and frequency.

2. The method of claim 1, wherein the mathematical function is defined by the following equation

y_i＝A_isin{Ψ_i}+S_i

Wherein, y_iIs the instantaneous displacement of said cutting tool (110) relative to C, A, at the ith cutting pass_iIs the maximum displacement, Ψ, of the cutting tool (110) relative to C_iIs y_iOf (a) and S_iIs y_iOf the starting position.

3. The method of claim 2, wherein

Where φ is a number in the closed interval between zero and 2 π,wherein N is a non-random, randomly or quasi-randomly selected positive or negative integerThe number of the whole numbers is an integer,is to correct lambda on the k-th subsequent cutting pass_iAn additional factor of phi_iIs a non-random, randomly or quasi-randomly selected number over a closed interval between zero and 2 pi radians.

4. The method of claim 2, further comprising, for a kth cutting pass after the ith cutting pass, translating an origin of the mathematical function by a distance S from the origin of the mathematical function on the ith cutting pass_i。

5. The method of claim 2, further comprising nonrandom, randomly, or quasi-randomly being a_iA value is assigned.

6. The method of claim 1, wherein the mathematical function is selected from a group of mathematical functions comprising a trigonometric function, a sawtooth function, and a square wave function.

7. The method of claim 2, wherein

Where phi is a number in a closed interval between zero and 2 pi radians,wherein N is a non-random, randomly or quasi-randomly selected positive or negative integer,is to correct lambda on the k-th subsequent cutting pass_iAn additional factor of phi_iIs a randomly or quasi-randomly selected number over a closed interval between zero and 2 pi radians, a_iAnd b_iIs a scalar quantity, Ω_iIs a non-random, randomly or quasi-randomly selected number over a closed interval between zero and 2 pi radians.

8. The method of claim 7, further comprising, for a kth cutting pass after the ith cutting pass, translating an origin of the mathematical function by a distance S from the origin of the mathematical function on the ith cutting pass_i。

9. The method of claim 6, further comprising nonrandom, randomly, or quasi-randomly being A_iAssigning a value, wherein Ai is the maximum displacement of the cutting tool (110) relative to the interval C.

10. The method of claim 1, wherein the step of causing relative motion between the cutting tool (110) and the surface of the workpiece (112, 114) comprises:

band-pass filtering a noise signal (104);

providing the band-pass filtered noise signal to a function generator (106);

generating a randomly modulated mathematical function by said function generator;

directing relative motion between the cutting tool (110) and the surface of the workpiece along the path on the surface of the workpiece (112, 114) in response to the function of the random modulation.

11. An optical substrate, comprising:

a surface (142) formed by a master surface machined by contacting a cutting tool (110) with a surface of a workpiece (112, 114);

for at least one cutting pass i, causing relative motion between the cutting tool and the surface of the workpiece along a path on the surface of the workpiece;

wherein the path (116, 122) is essentially a mathematical function defined over an interval C of a coordinate system, characterized by a set of non-random, random or quasi-random parameters selected from the group consisting of amplitude, phase and frequency;

forming a positive or negative electroform over the surface of the workpiece;

forming a stamp of the electroform; and

transferring the stamp of the electroform to an optical substrate.

12. A backlight display apparatus (300), comprising:

a light source (302) for generating light (306);

a light guide (304) for guiding said light (306) therealong;

a reflecting device (308) arranged along said light guide (304) for reflecting light (306) exiting said light guide (304);

an optical substrate (314) that receives light (306) from the light guide (304), the optical substrate (304) comprising:

a surface (142) formed by a master surface machined by contacting a cutting tool (110) with a surface of a workpiece (112, 114);

for at least one cutting pass i, causing relative motion between the cutting tool and the surface of the workpiece along a path on the surface of the workpiece;

wherein the path (116, 122) is essentially a mathematical function defined over an interval C of a coordinate system, characterized by a set of non-random, random or quasi-random parameters selected from the group consisting of amplitude, phase and frequency;

forming a positive or negative electroform over the surface of the workpiece;

forming a stamp of the electroform; and

transferring the stamp of the electroform to an optical substrate.

13. A master mold having a surface processed by the method of claim 1.

14. The method of claim 4, wherein the width w of the kth cutting pass is for the kth cutting pass after the ith cutting pass_kDifferent from the width of the ith pass.

15. The method of claim 14, wherein the width w of the kth cutting pass is such that for the kth cutting pass after the ith cutting pass_kThe difference relative to the ith pass is a gradient over all passes.

16. The method of claim 14, wherein for a kth cut after the ith cutting passCutting pass, width w of the k-th cutting pass_kThe difference relative to the i-th cut pass is random or quasi-random.

17. A backlight display apparatus (300), comprising:

a light source (302) for generating light (306);

a light guide (304) for guiding said light (306) therealong;

a reflecting device (308) arranged along said light guide (304) for reflecting light (306) exiting said light guide (304);

wherein the light guide (304) includes a surface (142) formed by a master surface machined by contacting a cutting tool with a surface of a workpiece;

for at least one cutting pass i, causing relative motion between the cutting tool and the surface of the workpiece along a path on the surface of the workpiece;

wherein the path (116, 122) is essentially a mathematical function defined over an interval C of a coordinate system, characterized by a set of non-random, random or quasi-random parameters selected from the group consisting of amplitude, phase and frequency;

forming a positive or negative electroform over the surface of the workpiece;

forming a stamp of the electroform; and

transferring the stamp of the electroform to an optical substrate.

18. The display device of claim 17, wherein for a kth cut pass after the ith cut pass, the width w of the kth cut pass_kDifferent from the width of the ith pass.

19. The display device of claim 18, wherein for a kth cut pass after the ith cut pass, the width w of the kth cut pass_kRelative to the ith cutting passThe difference in (c) is a gradient over all cutting passes.

20. The display device of claim 18, wherein for a kth cut pass after the ith cut pass, the width w of the kth cut pass_kThe difference relative to the i-th cut pass is random or quasi-random.

21. A method of machining a surface of a cylinder (112), the method comprising:

contacting a cutting tool (110) with the surface of the cylinder; and

for at least one cutting pass i, causing relative motion between the cutting tool (110) and the surface of the cylinder (112) to follow a path (116, 122) in a plane tangential to the surface of the cylinder (112);

wherein said path (116, 122) is essentially a mathematical function defined over an interval C of said cylinder characterized by a set of non-random, random or quasi-random parameters selected from the group consisting of amplitude, phase and frequency.