Making LED lighting directional: Synchronizing multiple surfaces

LED (Light-Emitting-Diode) is a semiconductor that can convert electrical energy into light energy. It changes the principle of tungsten filament light emission of incandescent lamps and three-primary color powder light emission of energy-saving lamps, and adopts electric field light emission. According to analysis, the characteristics of LED are very obvious, with long life, high light efficiency, no radiation and low power consumption. The spectrum of LED is almost entirely concentrated in the visible light band, and its luminous efficiency can exceed 150lm/W.

However, due to the large range of LED light output and the lower light energy per unit optical extension compared to traditional light sources, direct LED lighting in most cases is difficult to meet the performance indicators required by lighting fixtures and devices. Therefore, it is very necessary to conduct secondary optical design of lighting systems using LED as light sources.

Lighting systems are generally divided into reflective, refractive, total internal reflection and composite types. LED has a large range of emitted light, and it is difficult for reflective or refractive lighting systems to effectively adjust all the emitted light of the LED, while composite lighting systems are often not compact. TIR uses refraction and total internal reflection to effectively collect and adjust a large range of LED emitted light and ensure the compactness of the lighting system. This paper first designs a directional projector that can effectively collect and adjust LED light based on the synchronous multi-surface method and the law of conservation of optical extension; then, through a specific example, the structure and optical characteristics of this projector are analyzed and studied.

2 Etendue

The optical etendue describes the ability of an optical system to transmit light energy. The optical etendue of a beam is equal to the product of the beam in its angle and position area. In a plane where the three-dimensional coordinate z is equal to a constant, the optical etendue of a beam can be expressed as:

In the formula, P=nL, q=nM, where q is the refractive index of the medium in which the light beam is located, and L and M are the direction cosines of the light beam.

In Figure 1, the optical etendue emitted from the light source S1S2 and incident on the target T1T2 is:

Where S1T2 and S1T1 represent the optical path. The corresponding optical etendue in three dimensions is:

After the light beam passes through the ideal optical system, its optical extension remains unchanged, and all the light beams received by the system will be transmitted to the target surface.

3 Synchronous Multi-Surface Method

In general, for two given sets of light beams, there are two surfaces that make the incident light beams become corresponding outgoing light beams after being deflected. In two dimensions, the synchronous multi-surface method can be used to solve the contour curves corresponding to these two surfaces. The so-called synchronous multi-surface method means that the solution process of all the surfaces to be solved is carried out synchronously, and the completion of the solution of one of the surfaces to be solved means the completion of the solution of the remaining surfaces to be solved. The synchronous multi-surface method solves the points of the contour curve by solving point by point, and a point on one contour curve can be obtained by the obtained point on the other contour curve. This can be repeated to obtain two contour curves at the same time.

The synchronous multi-surface method is now described by taking the directional control of the light emitted by a light source as an example, as shown in FIG2 .

Curve AB and curve CD are the contour curves of surface AB and surface CD respectively, and medium n and medium n1 are two different media. Point S1 and point S2 are two edge points of light source S1 S2. The light beams emitted from point S1 and point S2 correspond to wavefront w1 and wavefront w2 respectively after being refracted by curve AB and curve CD. A point on one of the curves and the normal of the curve at that point are known (such as point Po and the normal of curve AB at point Po), as well as the optical path Z from point Sl (point S2) to wavefront Wl (wavefront W2).

After the edge ray S1Po is refracted by the curve AB, the refracted ray is PoPl. Based on the known conditions, the normal of point P and curve CD at point P1 can be obtained. After the edge ray S2P2 is refracted by the curve AB, the refracted ray is P2P1. Based on the normal of point P1 and curve CD at point P1 and the optical path, the normal of point P2 and curve AB at point P2 can be obtained.

By repeating this process, the points of curve AB and curve CD can be obtained at the same time, and then curve AB and curve CD can be obtained by fitting the obtained points.

When solving the contour curve using the synchronous multi-surface method, all edge rays of the light source should be considered, and it is required that each point on the contour curve, except for the endpoints, has only two edge rays passing through it. In Figure 2, light 1 and light 2 correspond to edge ray S2P2 and edge ray S1 Po, respectively. According to the edge ray principle, the emitted light of all light sources between edge ray S1 Po and edge ray S2P2 will be distributed between light 1 and light 2 after being refracted by curves AB and CD.

Therefore, the optical system designed using the synchronous multi-surface method can effectively collect and adjust the outgoing light of the extended light source.

4 Lighting system design

This paper aims to design a directional projector, which can effectively collect the output light of high-power LEDs and distribute the collected LED output light within a predetermined light distribution range on both sides of the optical axis after being acted upon by the projector.

Figure 3 is a schematic diagram of the projector. To facilitate design and processing, the curved surface EC is taken as a conical surface, and the slope of the contour curve EC should be selected to ensure that the light after total reflection by the curved surface FM and the curved surface NQ does not produce total reflection on the curved surface EC. The curved surfaces AB and CD can collect and adjust the light emitted from the light source at a small angle, and the curved surfaces AT, FM, TV and NQ can collect and adjust the light emitted from the light source at a large angle. It is known that the optical extension of the light source is E. According to the law of conservation of optical extension and formula (1), it can be obtained that:

Wherein: Xi is the predetermined light distribution angle, that is, the required maximum angle between the outgoing light after the projector and the optical axis, as shown in Figure 3; S is the projection area formed by the intersection of all light groups with wavefronts w1 and W2 at the light outlet of the projector (such as light 3 and light 4, light 5 and light 6 in the figure, etc.) in the plane perpendicular to the optical axis.

From the above formula, the projected area can be obtained as:

From Formula 5 and Figure 3, it can be seen that the angle θ determines the projection area S, which in turn determines the radius of the light outlet of the projector.

The design method of the projector is as follows: first, according to the light distribution of the high-power LED and the predetermined light distribution angle, combined with the law of conservation of optical etendue and the principle of edge light, the points on AB, CD, AT, FM, TV and NQ are solved using the synchronous multi-surface method; then the solved points are fitted to obtain the corresponding curves.

4.1 Refractive Surface to Refractive Surface Design

The light from the light source within a small angle incident on the curved surface AB is refracted by the curved surface AB and the curved surface CD to form a light distribution that meets the predetermined angle range. The design process of the curved surface AB and the curved surface CD is shown in Figure 4. The initial conditions are the starting point P0, the design coordinates of the longitudinal Figure 4 refraction surface to the refraction surface of the point P1, the wavefront w1 and the wavefront w2.

Considering the compactness of the projector, the size of the light source should be considered when selecting point Po. Based on point P0, the optical extension of the light beam emitted from the chip and incident on curve AB in two dimensions can be obtained by equation (2):

According to the law of conservation of optical etendue and the predetermined light distribution angle, the radius of the light outlet corresponding to the curve CD can be obtained:

In order to achieve effective collection and adjustment of all light beams incident on curve AB, it is required that the edge light S2Po is refracted by curve AB and incident on point P1 on curve CD, and then refracted by curve CD into an outgoing light with a wavefront of wl; the edge light S1Po is refracted by curve AB and incident on point P3 on curve CD, and then refracted by curve CD into an outgoing light with a wavefront of w1; the edge light S2P2 is refracted by curve AB and incident on point P1 on curve CD, and then refracted by curve CD into an outgoing light with a wavefront of %.

From the above requirements, it can be known that the curve segments P1P3 and PoP2 are both Cartesian ovals. According to Fermat's principle and the law of refraction, the points on the curve segments P1P3 and PoP2, as well as the normals of the curves at the obtained points, can be obtained. Point P3 can be used to obtain the optical path Z from the edge point S1 to the wavefront w1. After that, the synchronous multi-surface method is used to solve the curves CD and AB except the Cartesian oval. After obtaining the points on the left side of the optical axis of the curves AB and CD, the symmetric points of the obtained points about the optical axis can be obtained by symmetry. The obtained points on the curves AB and CD are fitted respectively to obtain the curves AB and CD.

4.2 Refractive Surface-Total Reflective Surface Design

There are two groups of curved surfaces in the projector to collect and adjust the outgoing light within a large angle of the light source. The first group is curved surface AT and curved surface FM, and the second group is curved surface TV and curved surface NQ.

First solve the first set of surfaces. The initial conditions are point R. and point R1. The determination of point R1 is shown in Figure 5. Light ray SlRo is incident on point R1 after refraction, and then refracted into light ray 8 by total reflection and line segment EC. Light ray 7 corresponds to light ray 8, and the extensions of light ray 7 and light ray 8 intersect at point G. Light ray S1 F1 is first incident on the endpoint C of line segment EC after total reflection, and then refracted into light ray 10 by line segment EC.

Corresponding to the light ray 10 is the light ray 9, and the extended lines of the light ray 9 and the light ray 10 intersect at point G2.

According to the law of conservation of optical etendue, the projection area formed by the intersection of all light rays emitted from the curved surface EC in the plane perpendicular to the optical axis can be obtained:

In order to ensure that all light rays totally reflected by surfaces FM and NQ can be emitted from surface EC, it is required that:

Where z1 and z2 are the horizontal coordinates of point G1 and point G2 respectively. When selecting point R1, in addition to its horizontal coordinate satisfying the above formula, the point should be located below the straight line EC, and the normal of curve AT at point Ro should make a larger angle with the positive direction of the 27 axis (generally around 3 rad). The larger the angle, the greater the downward trend of curve A, the shorter the projection length of curve AT on the z-axis, and the more compact the projector. After determining point R1 and obtaining the normal of curve AT at point Ro, the surface AT and surface FM can be solved. The solution process is shown in Figure 6.

In order to effectively collect and adjust all light beams incident on the curve AT, there should be Cartesian oval curve segments R1R3 and RoR2 at the starting ends of the curve AT and the curve FM, respectively. The solution process of the curve segment R1R3 and the curve segment RoR2 is the same as the solution process of the curve segment P1P3 and the curve segment PoP2 in FIG3 .

After that, the synchronous multi-surface method and the linear extension method can be used to solve the curve FM and the curve AT except the Cartesian oval. The so-called linear extension method means that when solving a point on the curve, the intersection of the incident light at that point and the tangent line of the curve at the previous point is defined as the point. For example, when determining point R5, the intersection of the straight line R2R5 and the tangent line of the curve FM at point R3 is regarded as point R5.

Considering the compactness of the projector, when solving the curve AT, it is required that the angle between the normal of the curve AT at all the solved points and the positive direction of the z-axis is large (generally α≥1.9rad). When α≥1.9tad at the solved point R2n on the curve AT, and α<1.9rad at the next point, the solution of the curve AT using the synchronous multi-surface method should be terminated, and a Cartesian oval curve segment R2n+1*2n+3 and a curve segment R2nR2n+2 are added to the end of the curve AT and the curve FM. Fitting the solved points on the curve AT and the curve FM respectively can obtain the curve AT and the curve FM.

Next, solve the second set of surfaces. The initial conditions are point Ho and point H1. The determination of point H1 is shown in Figure 7. Point G3 and point G4 are the intersection points of the extended lines of light 11 and light 12, and the intersection points of the extended lines of light 13 and light 14, respectively.

In order to make all the light rays totally reflected by the surface NQ emerge from the surface EC, it is required that

Where: z3 and z4 are the horizontal coordinates of point G3 and point G4 respectively; S09 is the projection area formed by the intersection of all light groups with wavefronts w1 and w2 emitted from surface CD in the plane perpendicular to the optical axis; SrTw is the projection area formed by the intersection of all light groups with wavefronts w1 and IV: refracted by surface EC after total reflection from surface FM in the plane perpendicular to the optical axis. When selecting point H1, the horizontal coordinate of point H1 is required to satisfy the above formula and be greater than the horizontal coordinate of point M (to facilitate mold opening during processing); point H1 should be located below curve FM; the angle between the normal of curve TV at point Ho and the positive direction of z axis is large (generally around 3rad). After determining point H1 and obtaining the normal of curve T1 at point H0, the solution of surface TV and surface NQ can be performed.

The solution process of curve IV and curve NQ is the same as that of surface AT and surface FM. When solving curve TV, since the angle between the normal line of curve IV at point H0 and the positive direction of the z-axis is large, and the ordinate of point H0 is often small, the solution of curve TV and curve NQ can be completed before the angle between the normal line of curve TV and the positive direction of the X-axis is less than 1.9 rad. After that, curve NQ and the calculated points on curves T, , are fitted respectively to obtain curve NQ and curve IV.

For the convenience of processing, use a line segment to connect point E and point F, and the horizontal coordinate of point E should be greater than the horizontal coordinate of point F; use a line segment to connect point M and point N. Then rotate the contour curve of the projector to obtain the three-dimensional model of the projector, and the design of the projector is completed.

5 Design Examples and Simulation Analysis

A 1×1㎡112 LED chip is used as the light source, and the projector is made of organic glass (PMMA). It is required that all the emitted light of the LED chip is distributed on both sides of the optical axis after being acted upon by the projector.

The end point of the inner refractive surface profile curve relative to the chip is taken as (-4, 6).

According to the above analysis, the points on each contour curve calculated are introduced into UG for curve fitting, and then the contour curve generated by fitting is rotated around the optical axis to obtain the three-dimensional model of the projector (Figure 8). Figure 8 is the cross-sectional dimensions of the projector, the diameter of the light outlet of the transmissive device is 31.5mm, and the height is 20.2mm. The three-dimensional model of the projector is then imported into Tracepro, and the LED output light is traced. Figure 9 is a ray tracing diagram of the system. Class I is a beam of LED output light distributed within a predetermined light distribution range after being acted upon by the projector, and Class II is a beam of LED output light formed by Fresnel reflection of each refractive surface. Figure 10 is an illumination distribution diagram of the target plane 50mm from the top of the projector.

The simulation analysis results show that:

(1) The system structure is very compact.

(2) The efficiency of the system is greater than 91% as shown in the ray tracing diagram of the system in Figure 9. The light energy loss is mainly caused by the Fresnel reflection of each refractive surface and the absorption of light energy by the material used in the projector.

(3) The projector effectively collects and directs all the light emitted by the LED.

6 Conclusion

This paper proposes a projector design method for effectively collecting and directional controlling the emitted light of high-power LEDs. According to the emitted light distribution of LEDs, the predetermined light distribution range and the law of conservation of optical extension, the points on the contour curves of each refractive surface and total reflection surface are obtained by using the synchronous multi-surface method. In UG, the obtained points are firstly fitted with curves, and the projector model and the surface shape data suitable for CNC machining are obtained by rotating the fitted curves. Then, the model is imported into Tracepro optical design software. Ray tracing is performed on the emitted light of U and D, and the efficiency of the system is analyzed and studied. The directional projector designed by this method has a compact structure and high light energy transmission efficiency, and can effectively collect and directionally control all the emitted light of UD.