A method for determining the major axis, minor axis and tilt angle of a color BIN one-step ellipse

Abstract

The present invention discloses a method for determining the major axis, minor axis, and tilt angle of a color BIN one-step ellipse, which is used to help LED packaging engineers quickly and effectively formulate LED white light binning standards, and at the same time provide a method fulcrum for LED color difference problems. The present invention proposes a method for using 1964CIE coordinates (u, v) and 1931CIE coordinates (x, y) to transform each other, and use mathematical thinking to model and calculate the major axis (a), minor axis (b), and tilt angle (θ) of the color BIN one-step ellipse. The present invention can help LED packaging engineers quickly and effectively formulate LED white light binning standards, and at the same time provide a method fulcrum for LED color difference problems.

Description

Technical Field

[0001] The invention relates to the technical field of LED packaging phosphor ratio, and in particular to a method for determining a major axis, a minor axis and an inclination angle of a color BIN one-step ellipse. Background Art

[0002] Currently, the white light LEDs on the market use the MacAdam ellipse BIN method, but this method requires looking up the diagram to know the g11, g12, and g22 parameters in order to calculate the major axis (a), minor axis (b), and tilt angle (θ) of the one-step ellipse, which will cause considerable trouble in our actual production application. Summary of the invention

[0003] The purpose of the present invention is to provide a method for determining the major axis, minor axis and tilt angle of a color BIN ellipse in one step. The method can obtain the above results through pure theoretical calculations of mathematical thinking, and is more simple to operate. It can help LED packaging engineers quickly and effectively formulate LED white light binning standards, and at the same time provide a method fulcrum for LED color difference problems to solve the problems raised in the above background technology.

[0004] To achieve the above object, the present invention provides the following technical solutions:

[0005] A method for determining the major axis, minor axis, and tilt angle of a color BIN one-step ellipse comprises the following steps:

[0006] Step 1: Define the color center coordinate point (x, y), and use the mathematical fitting method to calculate the color temperature CCT and 1964 CIE standard (u, v) coordinates corresponding to the center point;

[0007] Step 2: Draw a circle with the 1964CIE standard (u, v) coordinates calculated in step 1 as the center and 0.001 as the radius, and find the coordinates (u1, v1) corresponding to θ = 0°, the coordinates (u2, v2) corresponding to θ = 90°, the coordinates (u3, v3) corresponding to θ = 180°, and the coordinates (u4, v4) corresponding to θ = 270°;

[0008] Step 3: Convert the 1931 CIE standard (x, y) coordinates by the 1964 CIE (u, v) coordinate standard, and convert the (u1, v1), (u2, v2), (u3, v3), and (u4, v4) obtained in step 2) into the corresponding (x1, y1), (x2, y2), (x3, y3), and (x4, y4) coordinates by the 1964 CIE (u, v) coordinate standard and the 1931 CIE standard (x, y) coordinate conversion standard;

[0009] Step 4: Use the distance formula to calculate the distance A between the points (x2, y2) and (x4, y4) and the distance B between the points (x1, y1) and (x3, y3) obtained in step 3);

[0010] Step 5: Calculate the major axis of the color BIN one-step ellipse (a) through mathematical fitting function and piecewise function modeling;

[0011] Step 6: Obtain the minor axis of the color BIN one-step ellipse (b) through mathematical fitting function and piecewise function modeling;

[0012] Step 7: Use the point-slope method to calculate the slope K of the straight line at points (x2, y2) and (x4, y4), and use the ATAN (K) trigonometric function to calculate the inclination angle (θ) of the one-step ellipse.

[0013] Furthermore, the formula for step 1 is as follows:

[0014]

[0015]

[0016]

[0017] Furthermore, the calculation formula of step 2 is as follows:

[0018] u i =u+0.001*cosθ

[0019] v i =v+0.001*sinθ

[0020] Furthermore, the conversion standard formula of step 3 is as follows:

[0021]

[0022]

[0023] Furthermore, the calculation formula of step 4 is as follows:

[0024]

[0025]

[0026] Furthermore, the calculation formula of the major axis (a) of the color BIN one-step ellipse in step 5 is as follows:

[0027]

[0028] Furthermore, the calculation formula of the minor axis (b) of the color BIN one-step ellipse in step 6 is as follows:

[0029]

[0030] Furthermore, the calculation formula of the ellipse tilt angle (θ) in step 7 is as follows:

[0031]

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] The present invention helps LED packaging engineers to quickly and effectively formulate LED white light binning standards, and at the same time provides a method fulcrum for the LED color difference problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is the calculation software page of the method of the present invention;

[0035] Figure 2 The calculation result of the center point (0.4578, 0.4101) of the method of the present invention is compared with the MacAdam ellipse;

[0036] Figure 3 The calculation result of the center point (0.3818, 0.3798) of the method of the present invention is compared with the MacAdam ellipse;

[0037] Figure 4 This is a comparison between the calculation result of the center point (0.3123, 0.3282) of the method of the present invention and the MacAdam ellipse. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] like Figure 1 As shown, a method for determining the major axis, minor axis, and tilt angle of a color BIN one-step ellipse is used to help LED packaging engineers quickly and effectively formulate LED white light binning standards, and at the same time provide a method fulcrum for LED color difference problems. The present invention proposes a method for using 1964 CIE coordinates (u, v) and 1931 CIE coordinates (x, y) to convert each other, and use mathematical thinking to model and calculate the major axis (a) 12, minor axis (b) 13, and tilt angle (θ) 14 of the color BIN one-step ellipse. Figure 1In the figure, 1 represents the defined color center coordinate point (x, y), 2 represents the color temperature CCT corresponding to the center point, 3 represents the 1964 CIE standard (u, v) coordinate corresponding to the center point, 4 represents the coordinate (u1, v1) corresponding to θ=0°, 5 represents the coordinate (x1, y1) corresponding to θ=0°, 6 represents the coordinate (u2, v2) corresponding to θ=90°, 7 represents the coordinate (x2, y2) corresponding to θ=90°, 8 represents the coordinate (u3, v3) corresponding to θ=180°, 9 represents the coordinate (x3, y3) corresponding to θ=180°, 10 represents the coordinate (u4, v4) corresponding to θ=270°, 11 represents the coordinate (x4, y4) corresponding to θ=270°, 12 represents the major axis of the one-step ellipse (a), 13 represents the minor axis of the one-step ellipse (b), and 14 represents the inclination angle (θ) of the one-step ellipse.

[0040] 1) As a further optimization scheme for determining the major axis (a), minor axis (b), and tilt angle (θ) of a color BIN one-step ellipse described in the present invention, a color center coordinate point (x, y) is defined, and a mathematical fitting method is used to calculate the color temperature CCT corresponding to the center point and the 1964 CIE standard (u, v) coordinates;

[0041]

[0042]

[0043]

[0044] 2) As a further optimization scheme for determining the major axis (a), minor axis (b), and tilt angle (θ) of a color BIN one-step ellipse described in the present invention, a circle is drawn with the 1964CIE standard (u, v) coordinates calculated in step 1 as the center and 0.001 as the radius, and the coordinates (u1, v1) corresponding to θ=0°, the coordinates (u2, v2) corresponding to θ=90°, the coordinates (u3, v3) corresponding to θ=180°, and the coordinates (u4, v4) corresponding to θ=270° are obtained (the calculation method uses the following formula):

[0045]

[0046] 3) As a further optimization scheme for determining the major axis (a), minor axis (b), and tilt angle (θ) of a color BIN one-step ellipse described in the present invention, the 1931 CIE standard (x, y) coordinates are converted by the 1964 CIE (u, v) coordinate standard, and the (u1, v1), (u2, v2), (u3, v3), and (u4, v4) obtained in step 2) are converted into corresponding (x1, y1), (x2, y2), (x3, y3), and (x4, y4) coordinates by the 1964 CIE (u, v) coordinate standard and the 1931 CIE standard (x, y) coordinate conversion standard (the conversion standard is as follows):

[0047]

[0048] 4) Use the distance formula to calculate the distance A between (x2, y2) and (x4, y4) and the distance B between (x1, y1) and (x3, y3) obtained in step 3):

[0049]

[0050]

[0051] 5) As a further optimization scheme for determining the major axis (a), minor axis (b), and tilt angle (θ) of a color BIN one-step ellipse according to the present invention, the major axis (a) of the color BIN one-step ellipse is obtained by mathematical fitting function and piecewise function modeling:

[0052]

[0053] 6) Obtain the minor axis of the color BIN one-step ellipse through mathematical fitting function and piecewise function modeling (b);

[0054]

[0055] 7) As a further optimization scheme for determining the major axis (a), minor axis (b), and inclination angle (θ) of a color BIN one-step ellipse described in the present invention, the point-slope method is used to calculate the slope K of the straight line at the points (x2, y2) and (x4, y4), and the ATAN (K) trigonometric function is used to calculate the inclination angle (θ) of the one-step ellipse.

[0056]

[0057] For example:

[0058] 1) Calculate the center point (0.4578, 0.4101) color BIN one-step ellipse major axis (a), minor axis (b), tilt angle (θ) according to the above steps. The calculation results are as follows Figure 2 .

[0059] The calculation results of the present invention are as follows: the major axis (a) of the one-step ellipse is 0.00256, the minor axis (b) of the one-step ellipse is 0.00137, and the inclination angle (θ) of the one-step ellipse is 55.26°;

[0060] The parameters of the MacAdam ellipse at the center point (0.4578, 0.4101) are: the major axis of the one-step ellipse (a) is 0.00258, the minor axis of the one-step ellipse (b) is 0.00137, and the tilt angle of the one-step ellipse (θ) is 57.17°;

[0061] The actual tolerances of the two are consistent.

[0062] 2) Calculate the center point (0.3818, 0.3798) color BIN one-step ellipse major axis (a), minor axis (b), tilt angle (θ) according to the above steps. The calculation results are as follows Figure 3 .

[0063] The calculation results of the present invention are as follows: the major axis (a) of the one-step ellipse is 0.00313, the minor axis (b) of the one-step ellipse is 0.00134, and the inclination angle (θ) of the one-step ellipse is 58.77°;

[0064] The parameters of the MacAdam ellipse at the center point (0.3818, 0.3798) are: the major axis of the one-step ellipse (a) is 0.00313, the minor axis of the one-step ellipse (b) is 0.00134, and the tilt angle of the one-step ellipse (θ) is 54°;

[0065] The actual tolerances of the two are basically the same.

[0066] 3) Calculate the center point (0.3123, 0.3282) color BIN one-step ellipse major axis (a), minor axis (b), tilt angle (θ) according to the above steps. The calculation results are as follows Figure 4 .

[0067] The calculation results of the present invention are as follows: the major axis (a) of the one-step ellipse is 0.00223, the minor axis (b) of the one-step ellipse is 0.00095, and the inclination angle (θ) of the one-step ellipse is 61.23°;

[0068] The parameters of the MacAdam ellipse at the center point (0.3123, 0.3282) are: the major axis of the one-step ellipse (a) is 0.00223, the minor axis of the one-step ellipse (b) is 0.00134, and the inclination angle of the one-step ellipse (θ) is 58.23°; the actual tolerances of the two are basically the same.

[0069] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for determining the major axis, minor axis, and tilt angle of a color BIN one-step ellipse, characterized in that: The steps include: Step 1: Define the color center coordinate point (x, y), and use the mathematical fitting method to calculate the color temperature CCT and 1964 CIE standard (u, v) coordinates corresponding to the center point; Step 2: Draw a circle with the 1964CIE standard (u, v) coordinates calculated in step 1 as the center and 0.001 as the radius, and find the coordinates (u1, v1) corresponding to θ = 0°, the coordinates (u2, v2) corresponding to θ = 90°, the coordinates (u3, v3) corresponding to θ = 180°, and the coordinates (u4, v4) corresponding to θ = 270°; Step 3: Convert the 1931 CIE standard (x, y) coordinates by the 1964 CIE (u, v) coordinate standard, and convert the (u1, v1), (u2, v2), (u3, v3), and (u4, v4) obtained in step 2) into the corresponding (x1, y1), (x2, y2), (x3, y3), and (x4, y4) coordinates by the 1964 CIE (u, v) coordinate standard and the 1931 CIE standard (x, y) coordinate conversion standard; Step 4: Use the distance formula to calculate the distance A between the points (x2, y2) and (x4, y4) and the distance B between the points (x1, y1) and (x3, y3) obtained in step 3); Step 5: Calculate the major axis of the color BIN one-step ellipse (a) through mathematical fitting function and piecewise function modeling; The calculation formula for the major axis (a) of the color BIN one-step ellipse in step 5 is as follows: Step 6: Obtain the minor axis of the color BIN one-step ellipse (b) through mathematical fitting function and piecewise function modeling; The calculation formula for the color BIN one-step ellipse minor axis (b) in step 6 is as follows: Step 7: Use the point-slope method to find the slope K of the straight line at points (x2, y2) and (x4, y4), and use the ATAN (K) trigonometric function to find the inclination angle (θ) of the one-step ellipse; The mathematical fitting method formula of step 1 is as follows:

2. The method for determining the major axis, minor axis and tilt angle of a color BIN one-step ellipse according to claim 1, characterized in that: The calculation formula for step 2 is as follows: in i =u+0.001*cosθ v i =v+0.001*sinθ。 3. The method for determining the major axis, minor axis and tilt angle of a color BIN one-step ellipse as claimed in claim 1, characterized in that: The conversion standard formula for step 3 is as follows:

4. The method for determining the major axis, minor axis and tilt angle of a color BIN one-step ellipse as claimed in claim 1, characterized in that: The calculation formula for step 4 is as follows:

5. The method for determining the major axis, minor axis and tilt angle of a color BIN one-step ellipse as claimed in claim 1, characterized in that: The calculation formula for the ellipse tilt angle (θ) in step 7 is as follows: θ=ATAN(K).

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