# Patent

## Title
Symmetric serrated edge light guide having circular base segments

## Abstract

The present invention provides a planar light guide film for a backlight unit having at least one point light source, the light guide film comprising a light input surface for receiving light from the point light source, a light redirecting surface for redirecting light received from the light input surface and a light output surface for outputting at least the light redirected from the light redirecting surface. The light input surface further comprises a composite lens structure having a circular tip segment with a first contact angle, and a first and second circular base segments with a second contact angle, the second contact angle being greater than the first contact angle and the second contact angle being equal to each other. Further, the circular tip segment satisfies the following equation:

y1=a1+√{square root over ((r12−x2))}

and the circular base segments satisfies the following equations:

y2=b2+√{square root over ((r22−(x+a2)2))}

y3=b3+√{square root over ((r32−(x−a3)2))}.

## Background
FIELD OF THE INVENTION
The present invention relates to a light guide film of a light emitting diode (LED) backlight unit, and, more particularly, to a light guide film of an LED backlight unit, which has a plurality of grooves carved into an incident plane of the light guide film to increase an incidence angle of which light can be transmitted through the light guide film.
BACKGROUND OF THE INVENTION
Typically, a liquid crystal display (LCD) for handheld and notebook devices generally employs at least one lateral light emitting diode (LED) as a light source of a backlight unit. Such a lateral LED is generally provided to the backlight unit as shown in FIG. 1 of Yang U.S. Pat. No. 7,350,598.
Referring to FIG. 1, the backlight unit 10 comprises a planar light guide film 20 disposed on a substrate 12, and a plurality of lateral LEDs 30 (only one lateral LED is shown in FIG. 1) disposed in an array on a lateral side of the light guide film 20. Light L entering the light guide film 20 from the LED 30 is reflected upwardly by a minute reflection pattern 22 and a reflection sheet (not shown) positioned on the bottom of the light guide film 20, and exits from the light guide film 20, providing back light to an LCD panel 40 above the light guide film 20. Such a backlight unit 20 suffers from a problem as shown in FIG. 2 when light is incident on the light guide film 20 from the LED 30.
As shown in FIG. 2, light L emitted from each LED 30 is refracted toward the light guide film 20 by a predetermined angle θ due to difference in refractive index between media according to Snell's Law when the light L enters the light guide film 20. In other words, even though the light L is emitted at a beam angle of α1 from the LED 30, it is incident on the light guide film 20 at an incidence angle of α2 less than α1. In FIG. 3, such an incidence profile of light L is shown. Therefore, there is a problem of increasing the length (l) of a combined region where beams of light L entered the light guide film 20 from the respective LEDs 30 are combined. In addition, light spots H also called “hot spots” and dark spots D are alternately formed in the region corresponding to the length (l) on the incident plane of the light guide film 20. Each of the light spots H is formed at a location facing the LED 30, and each of the dark spots D is formed between the light spots H.
Since the alternately formed light and dark spots are not desirable for the light guide film, they should be minimized and the length (l) should be shortened as much as possible. For this purpose, it is necessary to increase an angle of light entering the light guide film, that is, an incidence angle of light.
For this purpose, it is suggested to form protrusions on the input surface of the light guide film as shown in FIG. 4. Specifically, a plurality of fine prism-shaped structures 24 or arc-shaped structures (not shown) are formed on a light input surface 20A of a light guide film 20 and light L enters the light guide film at an incidence angle α3 substantially equal to an orientation angle α1 of light emitted from a focal point F of a light source. Thus, if orientation angles α1 of light beams emitted from the focal point F of the light source are identical, the light L enters the light guide film at an incidence angle α3 wider than the case of FIGS. 2 and 3. However, with this solution, there is some secondary light collimation where the light rays are refracted by the wall of the adjacent prism or arc-shaped structure as shown in FIG. 4. Secondary light collimation from the walls of the adjacent prism structure turns the light ray back on-axis providing less diffusion of the light from the light source as shown in FIG. 4. Thus the continuous prism- or arc-shaped structures on the input surface have limited light diffusing capability.
Therefore an improved input edge design is needed to provide a more uniform surface illumination of the light guide film without sacrificing the efficiency of the backlight system.
SUMMARY OF THE INVENTION
The present invention is aimed at overcoming the problems (hot spots and secondary light collimation) associated with the above prior art and therefore yield a more uniform surface illumination of the light guide film without sacrificing the efficiency of the backlight system.
The present invention provides a planar light guide film for a backlight unit having at least one point light source, the light guide film comprising: a light input surface for receiving light from the point light source; a light redirecting surface for redirecting light received from the light input surface; a light output surface for outputting at least the light redirected from the light redirecting surface; wherein the light input surface further comprises a composite lens structure having a circular tip segment with a first contact angle, and a first and second circular base segments with a second contact angle, the second contact angle being greater than the first contact angle and the second contact angle being equal to each other; and wherein the circular tip segment satisfies the following equation:

y1=a1+√{square root over ((r12−x2))}

and the circular base segments satisfies the following equations:

y2=b2+√{square root over ((r22−(x+a2)2))}

y3=b3+√{square root over ((r32−(x−a3)2))}

In addition, the invention further provides a planar light guide film for a backlight unit having at least one point light source, the light guide film comprising: a light input surface for receiving light from the point light source; a light redirecting surface for redirecting light received from the light input surface; a light output surface for outputting at least the light redirected from the light redirecting surface; wherein the light input surface further comprises a composite lens structure having gaps there between, the lens structure having a circular tip segment with a first contact angle, and a first and second circular base segments with a second contact angle, the second contact angle being greater than the first contact angle and the second contact angle being equal to each other; and wherein the circular tip segment satisfies the following equation:

y1=a1+√{square root over ((r12−x2))}

and the circular base segments satisfies the following equations:

y2=b2+√{square root over ((r22−(x+a2)2))}

y3=b3+√{square root over ((r32−(x−a3)2))}

Further, the invention provides a planar light guide film for a backlight unit having at least one point light source, the light guide film comprising: a light input surface for receiving light from the point light source; a light redirecting surface for redirecting light received from the light input surface; a light output surface for outputting at least the light redirected from the light redirecting surface; wherein the light input surface further comprises a serrated lens structure that is provided only where the point light source is incident on the light input surface, the lens structure having a circular tip segment with a first contact angle, and a first and second circular base segments with a second contact angle, the second contact angle being greater than the first contact angle and the second contact angle being equal to each other; and wherein the circular tip segment satisfies the following equation:

y1=a1+√{square root over ((r12−x2))}

and the circular base segments satisfies the following equations:

y2=b2+√{square root over ((r22−(x+a2)2))}

y3=b3+√{square root over ((r32−(x−a3)2))}




BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows a schematic diagram illustrating a conventional backlight module;
FIG. 2 shows a schematic diagram illustrating the distribution of bright/dark bands of a conventional light guide plate;
FIG. 3 shows a schematic diagram illustrating an embodiment of conventional light-diffusing structures;
FIG. 4 shows a schematic diagram illustrating another embodiment of conventional light-diffusing structures;
FIGS. 5a and 5b shows a schematic diagram illustrating a light guide film according to an embodiment of the invention;
FIGS. 6a-6c show schematic diagrams illustrating the various segments of the composite lens feature according to an embodiment of the invention;
FIGS. 7a and 7b show schematic diagrams illustrating the light diffusing capability of the composite lens feature with a gap between each adjacent feature;
FIG. 8 shows another embodiment of this invention;
FIGS. 9a and 9b show the luminance intensity at various distances from the light input surface for a circular or arc shaped input feature;
FIGS. 10a and 10b show the luminance intensity at various distances from the light input surface for a trapezoidal feature or feature with slanted sides; and
FIGS. 11a and 11b show the luminance intensity at various distances from the light input surface according to an embodiment of the invention.



DETAILED DESCRIPTION OF THE INVENTION
A light guide film in accordance with the present invention comprises a light output surface, a light redirecting surface and at least one light input surface that joins the light output surface and the light redirecting surface. The light input surface comprises a plurality of concave features consisting of a composite lens array. Each of the composite lenses is separated by a gap that is a flat surface perpendicular to the light output surface. The composite lenses and gaps are disposed along the light input surface, and extend from the output surface to the light redirecting surface. Each of the composite lenses has a symmetric cross-section consisting of a tip portion comprising a circular tip segment with a first contact angle and a base portion comprising two tilted circular base segments each with a second contact angle, the second contact angle being greater than the first contact angle and where the radius for each of the two tilted circular base segments are equal.
According to the above embodiment, the geometrical profile of the composite lens allows for comparatively large light deflecting distances; that is, the composite lens structure has better light-diffusing capability. Thus, the distance between the point light source and the active area of the display can be shortened, and the dark spots between the point light sources can be minimized, with the brightness uniformity still being acceptable. The circular tip segment uniformly distributes the light in front of the discrete light source, typically a light emitting diode (LED). The two tilted circular base segments uniformly distribute the light between the LEDs. A smooth curvature of the circular tip segment and tilted circular base segments maximizes the uniformity of the light spatial distribution so that the light output is uniform. Further, it is also necessary that each two adjacent composite lens structures have a gap or flat therebetween so a greater degree of deflection on the propagation path of the incident light can be achieved to thereby increase the light-diffusing effect.
Referring to FIGS. 5a and 5b, a light guide film according to an embodiment of the invention is shown, wherein a planar light guide film 12 is used to receive and guide the light from at least one point light source (such as LEDs 14 shown in FIG. 5a). The side surface of the light guide film 12 next to the LED 14 forms a light input surface 12a. The top surface of the light guide film 12 that makes an angle with the light input surface 12a forms a light-emitting surface 12b, and the bottom surface opposite the light-emitting surface 12b forms a light-reflecting surface 12c. The light-reflecting surface 12c is comprised of a plurality of light reflecting structures. The light emitted from the LED 14 enters the light guide film 12 via the light input surface 12a and propagates inside the light guide film 12. Then, it is guided toward the light-emitting surface 12b by the light-reflecting surface 12c and finally exits the light guide film 12 through the light-emitting surface 12b. 
Further, a plurality of concave composite lens structures 16 are serrated on the edge of the light input surface 12a, with their longitudinal directions being parallel to each other and having a gap (G) between each adjacent composite lens structure 16. Referring now to FIGS. 6a, 6b and 6c, the light input surface 12a, facing the LED 14, of the composite lens structure 16 has a circular tip segment 16a, and two tilted circular base segments 16b and 16c, respectively. The circular tip segment 16a of the concave composite lens structure 16 is the segment furthest from the light input surface 12a. Although the composite lens features for the preferred embodiment of this invention are disposed in a concave direction on the light input surface, the composite lens may also be in a convex direction on the light input surface.
The length T1 is the distance between the intersections of the extensions of a tangent at the top of the circular base segments 16b and 16c, and a tangent of the circular tip segment 16a, where the tangent of the circular tip segment 16a is parallel to the light input surface 12a. The length T2 is the total width of the circular tip segment 16a taken where the circular tip segment 16a intersects each the two circular base segments 16b and 16c. Note, T2 is parallel to T1. The contact angle A1 is the contact angle of the circular tip segment 16a at the point where the circular tip segment intersects the circular base segment 16b. Contact angle A1 is preferably greater than 0.1 degrees and less than or equal to 85 degrees. Referring now to FIG. 6b, the gap G is the distance between each adjacent composite lens. Preferably, the gap G is less than or equal to 0.9 times the pitch P. The pitch P of the linear composite lens array is the distance along the light input edge which includes the gap G distance and the total width B of the composite lens. Preferably the pitch P is greater than or equal to 5 micrometers and less than or equal to 1 millimeter (mm) The total height H of the feature is measured from the light input edge to the tangent of the circular tip segment 16a. The total height H of the composite lens is greater than or equal to 3 micrometers and less than or equal to 1 millimeter. The light input surface 12a will have a surface finish of 10 nanometers to 2 micrometers. The surface finish of the concave composite lens structures 16 can be the same or different than the gap G portion between the features.
Advantageously, the shape of an XY section of the circular tip segment 16a satisfies the following expression (1):

y1=a1+√{square root over ((r12−x2))}  (1)

where the circular tip segment 16a has a first radius r1. The first radius r1 is defined as the quotient of half the distance T1 divided by the tangent of half the contact angle A1. The value a1 is defined as the total height H minus the radius r1 of the circular tip segment 16a. The value x is a value in the direction of the light input surface and is preferably set within the range of −r1×sin(A1)≦x≦r1×sin(A1). The value y1 is a value in the light propagation direction.

Referring now to FIG. 6c, the composite lens structure also comprises two tilted circular segments, namely a first circular base segment 16b and a second circular base segment 16c. Each circular base segment comprises two contact angles, a top contact angle and a bottom contact angle. The first circular base segment 16b has a top contact angle A21 and a bottom contact angle A22. The second circular base segment 16c has a top contact angle A31 and a bottom contact angle A32. The top contact angle A21 is created by a tangent to the first circular base segment 16b at the point where the circular tip segment 16a and the first circular base segment 16b intersect. The bottom contact angle A22 is created by a tangent to the first circular base segment 16b at the point where the first circular base segment 16b intersects the light input surface 12a. The top contact angle A21 of the first circular base segment 16b and the top contact angle A31 of the second circular base segment 16c are equal. The bottom contact angle A22 of the first circular base segment 16b and the bottom contact angle A32 of the second circular base segment 16c are equal. The contact angles for each of the two circular base segments 16b and 16c are larger than the contact angle A1 of the circular tip segment 16a. 
Advantageously, the shape of an XY section of the circular base segments 16b and 16c as shown in FIG. 6c satisfy the following expressions (2 and 3) respectively:

y2=b2+√{square root over ((r22−(x+a2)2))}  (2)

y3=b3+√{square root over ((r32−(x−a3)2))}  (3)

Wherein:

r2=H2/[cos(A21)−cos(A22)]

a2=[(T2+B)/2−H2×√{square root over ((16r22−(B−T2)2−4H22)/(B−T2)2+4H22))}{square root over ((16r22−(B−T2)2−4H22)/(B−T2)2+4H22))}]/2

b2=−√{square root over (r22−(B/2−a2)2)}

B=T2+r2×[sin(A22)−sin(A21)]+r3×[sin(A32)−sin(A31)]

r3=H2/[cos(A31)−cos(A32)]

a3=−[(T2+B)/2−H2×√{square root over ((16r32−(B−T2)2−4H22)/(B−T2)2+4H22))}{square root over ((16r32−(B−T2)2−4H22)/(B−T2)2+4H22))}]/2

b3=−√{square root over (r32−(B/2−a3)2)}

H2=H−r1×[1−cos/(A1)]

Thus, the first circular base segment 16b has a radius r2 and the second circular base segment 16c has a radius r3. Referencing FIGS. 6a and 6c, the radius r2 of the first circular base segment 16b is defined as the quotient of the height H2 of the first circular base segment 16b divided by the quantity the cosine of the contact angle A21 at the top of the first circular base segment 16b minus the cosine of the contact angle A22 at the bottom of the first circular base segment 16b. The height H2 of the first circular base segment 16b is equal to the total height H of the composite lens feature 16 minus the radius r1 of the circular tip segment 16a times the quantity 1 minus the cosine of contact angle A1 of the circular tip segment 16a. 
The parameter a2 is equal to one half the quotient of the quantity of one half the quantity the total width T2 of the circular tip segment 16a plus the total width B of the composite lens feature 16 minus the quantity the height H2 of the first circular base segment 16b times the square root of the quotient of the quantity 16 times the square of the radius r2 of the first circular base segment 16b minus the square of the quantity of the total width B of the composite lens feature 16 minus the width T2 of the circular tip segment 16a, minus 4 times the square of the total height H2 of the first circular base segment 16b divided by the square of the quantity of the total width B of the composite lens feature 16 minus the width T2 of the circular tip segment 16a, plus 4 times the square of the total height H2 of the first circular base segment 16b. 
The parameter b2 is equal to the negative square root of the quantity of the radius r2 of the first circular base segment 16b squared minus the quantity one half the total width B of the composite lens feature 16 minus the parameter a2 that quantity squared.
The coordinate x is a value in the direction of the light input surface or more specifically in the direction of the total width B of the composite lens feature 16 and is preferably set within the range of −B/2≦x≦−T2/2. The coordinate y2 is a value in the light propagation direction.
The total width B of the composite lens feature 16 is equal to the total width T2 of the circular tip segment 16a plus the quantity of the radius r2 of the first circular base segment 16b times the quantity sine of the contact angle A22 at the bottom of the first circular base segment 16b minus the sine of the contact angle A21 at the top of the first circular base segment 16b, plus the quantity of the radius r3 of the second circular base segment 16c times the quantity sine of the contact angle A32 at the bottom of the second circular base segment 16c minus the sine of the contact angle A31 at the top of the second circular base segment 16c. The contact angles for the composite lens feature can be described where A21=A31, A22=A32 and A1≦A22, A21. Preferably, A1≦A22, A21≦85 degrees.
Referencing FIGS. 6a and 6c the radius r3 of the second circular base segment 16c is defined as the quotient of the height H2 of the second circular base segment 16c divided by the quantity the cosine of the contact angle A31 at the top of the second circular base segment 16c minus the cosine of the contact angle A32 at the bottom of the second circular base segment 16c. The height H2 of the second circular base segment 16c is equal to the total height H of the composite lens feature 16 minus the radius r1 of the circular tip segment 16a times the quantity 1 minus the cosine of contact angle A1 of the circular tip segment 16a. 
The parameter a3 is equal to one half the quotient of the quantity of one half the quantity the total width T2 of the circular tip segment 16a plus the total width B of the composite lens feature 16 minus the quantity the height H2 of the second circular base segment 16c times the square root of the quotient of the quantity 16 times the square of the radius r3 of the second circular base segment 16c minus the square of the quantity of the total width B of the composite lens feature 16 minus the width T2 of the circular tip segment 16a, minus 4 times the square of the total height H2 of the second circular base segment 16c divided by the square of the quantity of the total width B of the composite lens feature 16 minus the width T2 of the circular tip segment 16a, plus 4 times the square of the total height H2 of the second circular base segment 16c. 
The parameter b3 is equal to the negative square root of the quantity of the radius r3 of the second circular base segment 16c squared minus the quantity one half the total width B of the composite lens feature 16 minus the parameter a3 that quantity squared.
The coordinate x is a value in the direction of the light input surface or more specifically in the direction of the total width B of the composite lens feature 16 and is preferably set within the range of T2/2≦x≦B/2. The coordinate y2 is a value in the light propagation direction.
FIG. 7a is a ray tracing for an array of a single composite lens feature 16 of this invention illustrating what happens to the light rays when the individual composite lens features are disposed on the light input surface 12a in a contiguous manner such that there is no gap G between adjacent composite lenses. FIG. 7b is a similar ray tracing, but where the individual composite lens feature is separated by a gap G between adjacent features. The gap G is preferably less than or equal to 0.9P where P (as shown in FIG. 6b) is the pitch of the composite lens feature on the input surface 12a. In FIG. 7a, where the composite lens features are adjacent each other along the input surface, some of the light rays will experience a secondary light collimation as they are refracted when they reach the side of the adjacent feature. This secondary light collimation detracts from the diffusion capability of the composite lens feature 16. In FIG. 7b, the composite lens features are separated by a gap G. The gap allows the light ray to continue in a diffuse manner and thus widens the angle at which the light propagates in the light guide film. There is minimal secondary light collimation when the gap between features is incorporated into the composite lens feature design. In this way, the wider angle of light helps to mitigate the hot spots along the input surface of the light guide film.
Referring now to FIG. 8, the light guide film 12 in FIG. 8 shows the composite lens features 16 not disposed along the entire input surface 12a. Instead, the composite lens features 16 are disposed along the light input surface 12a in the region where the LED 14 light is incident. The luminance uniformity of the system is minimally affected as the unpatterned region on the light input surface has minimal light rays in this region.
EXAMPLES
FIG. 9a shows a portion of the light input surface 32 of a light guide film 30 with an arc- or circular-type structure 36. The graph in FIG. 9b illustrates the light intensity for the light guide film 30 at distances 3.5 mm, 4.5 mm and 5.5 mm from the light input surface 32. FIG. 9b shows that the localized light intensity decreases as the distance increases from the light input surface, but there are still some hot spots evident at 5.5 mm The arc- or circular-type structure solution provides some improvement for hot spots but is more effective at collimating light in line with the LED than widening the incidence angle. This is evident in the graph in FIG. 9b. In FIG. 9b, the LEDs are located at each of the vertical dotted lines and the light distribution is still not leveled out at 5.5 mm into the light guide film. It is apparent from the graph in FIG. 9b that the arc- or circular-type solution has insufficient diffusion capability.
FIG. 10a shows a portion of the light input surface 42 of a light guide film 40 with a composite lens structure that has flat slanted sides 46. This result would also be applicable to a trapezoidal shaped light input structure. The graph in FIG. 10b illustrates the light intensity for the light guide film 40 at distances 3.5 mm, 4.5 mm and 5.5 mm from the light input surface 42. FIG. 10b shows that the localized light intensity actually inverts in the area immediately in front of the LEDs, resulting in a dark spot immediately in front of the LEDs. This overall loss of light intensity immediately in front of the LED is due to the fact that the straight slanted walls diffuse the light more readily through the sides than through the tip. It is also noted that the shape of the light intensity profile across the light guide film does not change significantly as the distance increases from the input surface 42.
FIG. 11a shows a portion of the light input surface 52 of a light guide film 50 with the composite lens feature 56 of this invention. The composite lens feature utilizes a circular tip segment and two tilted circular base segments. The radius of each of the two tilted circular base segments is equal. The bottom contact angle of each of the two tilted circular base segments is greater than the contact angle of the circular tip segment. The circular tip segment uniformly distributes the light in the area immediately in front of the LED. The two tilted circular base segments uniformly distribute the light between the LEDs. The smooth curvatures of the circular tip segment and the two tilted base segments maximize the uniformity of the light spatial distribution so the output light is uniform. The graph in FIG. 11b illustrates that the composite lens 56 of the present invention generates uniform light output across the light guide film at distances of 3.5 mm, 4.5 mm and 5.5 mm from the input surface 52.
Hence, an improved light guide film is provided with symmetric light redirecting features to improve light output uniformity without sacrificing light input efficiency. Namely, the improved light guide film 12 having composite lens structure 16 provides enhanced light diffusion in the plane parallel to the light extraction plane and light reflection plane (top and bottom surfaces), allowing greater light redistribution between discrete light sources (light traveling outside the critical angle of planar un-serrated input edge), so that the light output uniformity is improved. Moreover, the light distribution in the plane perpendicular to the light extraction plane and light reflection plane (top and bottom surfaces) is minimized, so that the condition of the total internal reflection is minimized for the inputted traveling light.

## Claims

1. A planar light guide film for a backlight unit having at least one point light source, the light guide film comprising:
a light input surface for receiving light from the point light source;
a light redirecting surface for redirecting light received from the light input surface;
a light output surface for outputting at least the light redirected from the light redirecting surface;
wherein the light input surface further comprises a composite lens structure having a circular tip segment with a first contact angle, and a first and second circular base segments with a second contact angle, the second contact angle being greater than the first contact angle and the second contact angle being equal to each other; and
wherein the circular tip segment satisfies the following equation:


y1=a1+√{square root over ((r12−x2))}


and the circular base segments satisfies the following equations:


y2=b2+√{square root over ((r22−(x+a2)2))}



y3=b3+√{square root over ((r32−(x−a3)2))}.

2. The planar light guide film of claim 1 wherein the composite lens structure has a pitch P greater than or equal to 5 micrometers and less than or equal to 1 millimeter.

3. The planar light guide film of claim 2 wherein the composite lens structure has a gap G less than or equal to 0.9 times the pitch P.

4. The planar light guide film of claim 1 wherein the composite lens structure has a total height H greater than 3 micrometers and less than or equal to 1 millimeter.

5. The planar light guide film of claim 1 wherein the circular tip segment of the composite lens structure has a contact angle A1 greater than 0.1 degrees and less than or equal to 85 degrees.

6. The planar light guide film of claim 5 wherein the composite lens structure further comprises contact angles A21, A31, A22, and A32 wherein A21=A31, A22=A32 and A1≦A22.

7. A planar light guide film for a backlight unit having at least one point light source, the light guide film comprising:
a light input surface for receiving light from the point light source;
a light redirecting surface for redirecting light received from the light input surface;
a light output surface for outputting at least the light redirected from the light redirecting surface;
wherein the light input surface further comprises a composite lens structure having gaps there between, the lens structure having a circular tip segment with a first contact angle, and a first and second circular base segments with a second contact angle, the second contact angle being greater than the first contact angle and the second contact angle being equal to each other; and
wherein the circular tip segment satisfies the following equation:


y1=a1+√{square root over ((r12−x2))}


and the circular base segments satisfies the following equations:


y2=b2+√{square root over ((r22−(x+a2)2))}



y3=b3+√{square root over ((r32−(x−a3)2))}.

8. The planar light guide film of claim 7 wherein the circular tip segment of the composite lens structure has a contact angle A1 greater than 0.1 degrees and less than or equal to 85 degrees.

9. The planar light guide film of claim 8 wherein the composite lens structure further comprises contact angles A21, A31, A22, and A32 wherein A21=A31, A22=A32 and A1≦A22.

10. A planar light guide film for a backlight unit having at least one point light source, the light guide film comprising:
a light input surface for receiving light from the point light source;
a light redirecting surface for redirecting light received from the light input surface;
a light output surface for outputting at least the light redirected from the light redirecting surface;
wherein the light input surface further comprises a serrated lens structure that is provided only where the point light source is incident on the light input surface, the lens structure having a circular tip segment with a first contact angle, and a first and second circular base segments with a second contact angle, the second contact angle being greater than the first contact angle and the second contact angle being equal to each other; and
wherein the circular tip segment satisfies the following equation:


y1=a1+√{square root over ((r12−x2))}


and the circular base segments satisfies the following equations:


y2=b2+√{square root over ((r22−(x+a2)2))}



y3=b3+√{square root over ((r32−(x−a3)2))}.