2.1 Geometric-optical analysis
Traditional methodology
Due to the directional nature of light, its path can be accurately estimated using ray tracing calculations. Ray-tracing software, such as LightTools and Tracepro [18–20] has been developed to assist designers in addressing more complex challenges. One of the most advanced methods in optical design is freeform design. Various articles highlight the fundamental approach to designing a programming process that enhances efficiency and success in tackling larger-scale problems.
This basic method adheres to Snell's Law and encompasses four key components: (1) definition of the target pattern, (2) geometrical boundary conditions, (3) the relative size between the light source and the optical component, and (4) the calculation using the reverse of Snell's Law.
According to the statements above, all these processes can be encapsulated by formula (1). The application of the reverse Snell's Law can be expressed as an operation⊛ (reverse Snell's Law). The outcomes of freeform design can be represented by [freeform matrix], [Target image], and [Point source], respectively [21].
[freeform matrix]=[Target image]⊛(reverse Snell' s law)[Point source]………………….(1)
2.2 Revised freeform design rule
Concept of revised methodology
Although the reverse-Snell's law method offers an efficient solution for executing optical designs, it encounters challenges when addressing near-field issues.[22] T This is because the reverse-Snell's law assumes that all rays originate from the same point, necessitating that the optical device's geometrical size be significantly larger than the light source. In response to these limitations, this paper proposes a revised model to apply the freeform method to LED shape design, making the LEDs suitable for BLU applications. The model introduces a set of formulas, designated as formulas (2) to (4). Formula (2) outlines the process of ray tracing simulation, indicating that a light class is comprised of light rays after passing through a free-form surface, with the symbol "⊗ (ray trace)" denoting the ray tracing operation. However, formula (1), based on the reverse-Snell's law, is applicable only to point light sources and struggles with the consideration of light source volume in the context of backlight module applications. Thus, to design a general free-form surface model for surface light sources, we introduce the method of objective function correction. This involves modifying the objective function to an effective target image, aiming to incorporate this effective target image and point source into formula (1). The resulting freeform matrix should enable the original target image to achieve the desired outcome after undergoing the ray tracing process defined in formula (2).
To enhance this method, we introduce the concept of energy conservation. A difference curve is generated by comparing the simulation results produced by formula (2) with the objective function at each iteration. Utilizing the principle of normalization of the total area, we adjust the energy increase and decrease for each group of positions. This correction forms an effective target image that meets the requirements of the new objective function.
[Image]= [freeform matrix]⊗(ray trace)[Light source]……………………..………………..(2)
[Target image]=[Effective target image]⊛(reverse-Snell's law)[Point source]⊗(ray trace)[Light source]………………(3)
[Effective target image]=[Energy conservation fix]⊘[Target image]………...........………..(4)
Design flow
This paper presents the FDCSP structure, designed to integrate LEDs and lenses effectively. The schematic diagrams of the FDCSP are depicted in Fig. 1(a) and (b), illustrating the device's two noteworthy characteristics. Firstly, a white CSP is centrally embedded on the substrate's surface, ensuring a compact and efficient light source integration. Secondly, the device features a freeform-designed surface, optimizing light distribution and focusing. Together, these characteristics enable the FDCSP to function as an integrated device, combining the benefits of an LED with those of a secondary lens.
The design flow chart for the FDCSP, depicted in Fig. 2, outlines the systematic approach undertaken in this project.
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Initialize the design process by setting the environmental and object parameters in LightTools, with the main parameters outlined in Table 1.
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Derive the target function from the image to generate the initial freeform surface design.
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Import the initial freeform surface into the LightTools model to commence ray tracing simulation.
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Evaluate the simulation results by comparing them against the target function.
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Apply the principle of energy conservation to formulate an effective target function.
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Use the effective target function to create a revised freeform surface.
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Repeat the process of importing the freeform surface into the LightTools model for ray tracing simulation (step 2), and then evaluate the simulation results by comparing them with the target function (step 3). During this iterative process, calculate the Normalized Correlation Coefficient (NCC) using formula 5, where Xmn and Ymn represent the values of the experimental and simulated data, respectively, and X and Y denote the mean values of the experimental and simulated data across the angular range. It's essential to ensure that all simulation curves, across various Correlated Color Temperatures (CCT), achieve an NCC index of at least 99%. If the NCC is greater than or equal to the threshold value, proceed to step (7). If the NCC does not meet the threshold value, move to step (8) for further adjustments.
This step is crucial for verifying the accuracy and reliability of the freeform surface design against the intended target function, ensuring that the design meets the high standards required for practical application.
$$NCC=\frac{\sum _{m}\sum _{n}({X}_{mn}-\stackrel{-}{X})({Y}_{mn}-\stackrel{-}{Y})}{\sqrt{\left[\sum _{m}\sum _{n}{({X}_{mn}-\stackrel{-}{X})}^{2}\right]\left[\sum _{m}\sum _{n}{({Y}_{mn}-\stackrel{-}{Y})}^{2}\right]}}$$
5
…………………………………….….……….
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Break the loop and complete the design flow.
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Repeat steps (4) to (6).
Table. 1 The mainly parameters on the LightTools
Figure 3(a) displays an image of a single sample captured by a CCD camera on the module. Image processing techniques are then employed to calculate the light intensity profile of the spot, as shown in Fig. 3(b). This profile is subsequently utilized to further refine and continue the algorithm design. This revision aims to succinctly describe the methodological steps taken from capturing an image of the sample to analyzing its light intensity profile for use in ongoing algorithm development.