Projection optical system, optical system, and image projection device

Abstract

The aim is to achieve both low transistor (TR) and reduced temperature drift by designing some of the lenses constituting the projection optical system to have a shape that is less susceptible to deformation due to temperature. [Solution] The projection optical system of the present invention comprises a first lens group having negative refractive power, a second lens group having positive refractive power, and a reflective member positioned on the magnifying side of the projection optical system, wherein at least one lens in the first lens group is a resin aspherical lens, and the cross-sectional shape of the aspherical lens has a central part of the lens optical axis and a peripheral part located on the outer periphery of the central part and represented by an approximate polynomial of a hyperbolic surface, and the junction of the central part and the peripheral part is positioned on the lens optical axis side of the portion of the aspherical lens with high image plane movement sensitivity.

Description

[Technical Field]

[0001] The present invention relates to a projection optical system, an optical system, and an image projection device. [Background technology]

[0002] In optical devices such as projectors and other image projection equipment that use projection optics, several methods have been devised to solve problems such as installation location constraints and the inclusion of the speaker's shadow, by projecting onto a large screen from an extremely close distance. In such ultra-short-throw projection optical systems, the throw ratio (Tr), which is the ratio of the distance from the projector to the screen divided by the width of the image projected onto the screen, is used as an indicator. In ultra-short-throw projection optical systems with Tr = 0.6 or less, free-form lenses and free-form mirrors are frequently used to miniaturize the optical system itself while meeting the required optical performance (see, for example, Patent Documents 1 and 2). On the other hand, it is generally known that in short-focus optical systems, the power of each lens is large, and especially when using free-form lenses, they are susceptible to the effects of temperature changes. The variation in the image formation position at the imaging plane caused by temperature changes, including thermal expansion and distortion, is called thermal drift, and it was known that the effect of thermal drift at the edges of the screen is particularly large in ultra-short focal length projection optical systems.

[0003] One known method for realizing an optical system with low temperature drift is to suppress the degradation of lens characteristics due to heat by reducing the power of the lens (see, for example, Patent Document 3). On the other hand, simply reducing power, while advantageous for reducing temperature drift, is not suitable for achieving both low transistors and reduced temperature drift.

[0004] Another approach is to use lens materials with a low coefficient of thermal expansion; however, developing high-quality optical materials is currently difficult because it directly impacts costs. [Overview of the project] [Problems that the invention aims to solve]

[0005] The present invention aims to solve the above-mentioned problems by making a part of the lens constituting the projection optical system less susceptible to deformation due to temperature, thereby achieving both low transistor and reduced temperature drift. [Means for solving the problem]

[0006] The projection optical system of the present invention is a projection optical system comprising a plurality of lenses that magnifies and projects an image displayed on the image display surface of an image display element onto a projection surface as a projected image, wherein the projection optical system comprises a first lens group having negative refractive power, a second lens group having positive refractive power, and a reflective member positioned on the magnification side of the projection optical system, wherein at least one lens in the first lens group is an aspherical lens made of resin, and the cross-sectional shape of the aspherical lens has a central part of the lens optical axis and a peripheral part located on the outer periphery of the central part and represented by an approximate polynomial of a hyperbolic surface, and the junction of the central part and the peripheral part is positioned on the lens optical axis side of the portion of the aspherical lens with high image plane movement sensitivity. [Effects of the Invention]

[0007] According to the present invention, by making a part of the lenses constituting the projection optical system a shape that is less susceptible to deformation due to temperature, it is possible to achieve both low transistor and reduced temperature drift. [Brief explanation of the drawing]

[0008] [Figure 1] This figure shows an example of the configuration of an image projection device as a first embodiment of the present invention. [Figure 2] This figure shows a schematic diagram of the lens configuration of the projection optical system of the image projection device shown in Figure 1. [Figure 3] This figure shows the concept of the ray matrix of the projection optical system in this embodiment. [Figure 4] In the lens configuration shown in FIG. 2, it is a diagram numerically showing the influence amount of off-axis rays. [Figure 5] It is a diagram showing a reference example of conventional fitting conditions. [Figure 6] It is a diagram schematically showing the influence of temperature drift before and after thermal expansion in a spherical lens. [Figure 7] It is a diagram schematically showing the influence of temperature drift on the conic surface of an aspherical lens. [Figure 8] It is a diagram showing an example of the configuration of a portion with high image plane movement sensitivity and the lens surface shape in Numerical Example 1 of the present invention. [Figure 9] It is a diagram showing another example of the configuration of a portion with high image plane movement sensitivity and the lens surface shape in Numerical Example 1 of the present invention. [Figure 10] In Numerical Example 1 of the present invention, it is a diagram showing an example of longitudinal aberration on the projection plane. [Figure 11] In Numerical Example 1 of the present invention, it is a diagram showing an example of lateral aberration on the projection plane. [Figure 12] In Numerical Example 1 of the present invention, it is a diagram showing an example of lateral aberration on the projection plane. [Figure 13] In Numerical Example 1 of the present invention, it is a diagram showing an example of lateral aberration on the projection plane. [Figure 14] In Numerical Example 1 of the present invention, it is a diagram showing an example of lateral aberration on the projection plane. [Figure 15] It is a diagram showing an example of the lens configuration in Numerical Example 2 of the present invention. [Figure 16] In Numerical Example 2 of the present invention, it is a diagram showing an example of longitudinal aberration on the projection plane. [Figure 17] In Numerical Example 2 of the present invention, it is a diagram showing an example of lateral aberration on the projection plane. [Figure 18] In Numerical Example 2 of the present invention, it is a diagram showing an example of lateral aberration on the projection plane. [Figure 19] In Numerical Example 2 of the present invention, it is a diagram showing an example of lateral aberration on the projection plane. [Figure 20] This is a diagram showing an example of the configuration of a portion with high image plane movement sensitivity and the lens surface shape in Numerical Example 2 of the present invention. [Figure 21] This is a diagram showing another example of the configuration of a portion with high image plane movement sensitivity and the lens surface shape in Numerical Example 2 of the present invention. [Figure 22] This is a diagram showing an example of the approximation curve of the lens surface shape and the conic surface in Numerical Example 2 of the present invention. [Figure 23] This is a diagram showing another example of the approximation curve of the lens surface shape and the conic surface in Numerical Example 2 of the present invention. [Figure 24] This is a diagram showing an example of a lens configuration which is a reference example of the present invention. [Figure 25] This is a diagram showing an example of longitudinal aberration on the projection surface in Numerical Example 3. [Figure 26] This is a diagram showing an example of lateral aberration on the projection surface in Numerical Example 3. [Figure 27] This is a diagram showing an example of lateral aberration on the projection surface in Numerical Example 3. [Figure 28] This is a diagram showing an example of lateral aberration on the projection surface in Numerical Example 3. [Figure 29] This is a diagram showing an example of lateral aberration on the projection surface in Numerical Example 3. [Figure 30] This is a diagram showing an example of the configuration of a portion with high image plane movement sensitivity and the lens surface shape in Numerical Example 3 of the present invention. [Figure 31] This is a diagram showing another example of the configuration of a portion with high image plane movement sensitivity and the lens surface shape in Numerical Example 3 of the present invention.

Mode for Carrying Out the Invention

[0009] FIG. 1 is a diagram showing an example of an image projection apparatus 100 as one embodiment of the present invention. The image projection apparatus 100 includes a light source 101 that emits a light beam, and an image display element 102 that displays an image to be projected onto an image display surface and imparts image information to the transmitted light beam. The image projection device 100 also includes a lens unit 130 equipped with a projection optical system for projecting an image onto a screen 104 which is the projection surface, and a control unit 109 for controlling an image display element 102 to display the image to be projected onto the screen 104. The screen 104 is the projection surface onto which the image projection device 100 of the present invention projects an image.

[0010] The light source 101 emits white light in approximately parallel directions using a halogen lamp, which is a light source that emits light rays. Here, a metal halide lamp, a high-pressure mercury lamp, or an LED may also be used as the light source. The light source 101 is a white light source, but it may also be a light source that uses multiple monochromatic light sources such as laser light sources and combines the light converted to wavelengths corresponding to one or more basic colors such as R, G, and B, or a light source that combines the converted light with the monochromatic light from the laser light source.

[0011] The image display element 102 is an image display means that provides image information by transmitting an incident light beam, applying spatial modulation, and emitting it. In this embodiment, it is a reflective spatial light modulation element such as a DMD (Digital Micromirror Device). The image display element 102 may be a liquid crystal panel, or it may be a self-luminous light-emitting array. Furthermore, the image display element 102 may display an image input from an external device such as a computer, or it may display image data configured by a control unit located inside the image projection device.

[0012] The configuration of the lens unit 130 will be explained using Figure 2. The direction of the lens optical axis O of the lens unit 130 is defined as the Z-axis, and among the directions perpendicular to the Z-axis, the axis parallel to the vertical direction of the paper in Figure 2 is defined as the Y-axis, and the axes perpendicular to the Z-axis and Y-axis are defined as the X-axis. For the X-axis, Y-axis, and Z-axis, the direction of the arrows shown in Figure 2 is defined as the positive direction.

[0013] As shown in Figure 2, the lens unit 130 has a plurality of lenses LN1 to LN17 arranged on the Z axis to constitute the projection optical system 30. In other words, in this embodiment, the lens unit 130 constitutes a projection optical system that "includes multiple lenses and magnifies and projects an image displayed on the image display surface of the image display element 102 onto the screen 104, which is the projection surface." In Figure 2, the lens unit 130 is shown to include a concave mirror 39, but the configuration is not limited to this.

[0014] The projection optical system 30 is an optical system composed of multiple lenses LN1 to LN17. A concave mirror 39 is positioned as a reflective element at the widest point of the projection optical system 30, i.e., in the direction of optical path propagation, and is configured to project light toward the screen 104 using the concave mirror 39. The projection optical system 30 can be divided into a first lens group 31 consisting of multiple lenses LN1 to LN5, and a second lens group 32 consisting of multiple lenses LN6 to LN17, starting from the magnification side. The refractive power of the first lens group 31 is negative, and the refractive power of the second lens group 32 is positive.

[0015] Of the lenses LN1 to LN17 of the present invention, LN2, which is provided in the first lens group 31, and LN3, which is also arranged in the first lens group 31, are both aspherical lenses made of plastic (resin). Furthermore, the LN16 lens, which is located in the second lens group 32, is also a plastic aspherical lens. The distance (D), radius of curvature (R), and refractive index (N) of each lens will be discussed later.

[0016] As previously mentioned, in general, short-focus optical systems have high power from each lens, and are particularly susceptible to temperature drift when using free-form lenses. Now, let's consider a method for calculating the magnitude of the temperature drift effect for each lens. First, the ray matrix M, which is the so-called ABCD matrix of the entire projection optical system 30, is expressed as the product of the matrices in reverse order of the direction of light propagation, as shown in equation (1), where L is the matrix for a certain lens surface, Fr is the matrix up to that lens surface, and Re is the matrix after that lens surface.

[0017]

number

[0018] As shown in Figure 3, when the image position (x',u') and object position (x,u) are on the screen 104, equation (2) holds true for the entire optical system.

[0019]

number

[0020] In other words, from equations (1) and (2), the influence of a certain lens LN's matrix L on the image position can be determined by taking the derivative with respect to p when matrix L is replaced with matrix L × Δp for the entire ray matrix M. Furthermore, in this case, Δp is a matrix as shown in equation (3).

[0021]

number

[0022] Figure 4 shows the numerical calculation results that visually represent the shift in the image formation position on the screen 104 when the power of lens LN2 is changed by 0.0001 using such a ray matrix. In Figure 4, the enlarged side of LN2, i.e., the side facing screen 104, is referred to as the L2R1 plane, and the reduced side of LN2, i.e., the side facing image display element 102, is referred to as the L2R2 plane. As is clear from Figure 4, the higher the incident image height, that is, the further the incident position of the light ray to lens LN2 is radially away from the optical axis of lens LN2, the greater the change in the image plane position on screen 104 in response to the change in the power of LN2.

[0023] Furthermore, as can be seen from Figure 4, the change in the image plane position is particularly pronounced in the tangential direction, which is indicated as the TAN image plane. This direction represents the blurring of the image in the radial direction from the optical axis of lens LN2. Therefore, the present invention aims to reduce the effect of temperature drift so that blurring in the radial direction is reduced in the region where the amount of displacement δ of the image formation position in the radial direction of the lens optical axis in response to such changes in refractive power becomes large.

[0024] Now, while we speak of reducing temperature drift in general terms, various methods have been devised to achieve this. For example, Patent Document 3 presents a method for reducing the amount of fluctuation in refractive power when temperature drift occurs by keeping the power of the lens itself low. However, simply reducing power, while beneficial for reducing temperature drift, does not align with the objective of achieving both low transistors and reduced temperature drift. Alternatively, one could consider developing optical materials with a low coefficient of thermal expansion and a high refractive index, but developing such optical materials is difficult because it would be reflected in the cost. In this embodiment, the goal is to achieve both low transient response (TR) and reduced temperature drift while reducing costs, particularly by using plastic aspherical lenses. Therefore, the above-described method could not solve this problem.

[0025] Now, in the design phase for forming aspherical lenses, when creating typical resin aspherical lenses, a widely used method is to define a reference base surface and then create an approximate curve of the lens surface by defining the perturbation component from the base surface using the aspherical coefficient. For example, the conic constant K and the radius of curvature R of the conic surface. K This involves determining the aspherical coefficient, etc.

[0026] Since it is impossible to create a lens that perfectly meets optical performance requirements, when using this method, numerical calculations are often fitted to the base surface so that the area near the optical axis center of the lens, where the influence of aberrations and light intensity tend to be large, closely matches the base surface when forming the approximation curve. In this case, as schematically shown in Figure 5, the base surface tends not to coincide very well with the optical axis of the lens at positions away from the optical axis center.

[0027] However, in a configuration like that of this embodiment, as shown in Figure 4, it has been found that light rays passing away from the optical axis center of the lens (off-axis rays) significantly affect the change in the image formation position at the edge of the screen 104. Therefore, in this embodiment, when designing the curved surface of the aspherical lens LN2, in addition to the aberration condition of the lens center 41, which is near the lens optical axis, the peripheral portion 42, which is the outer part of the lens that is off the lens optical axis, is approximated as a base surface by a hyperbolic surface where the conic constant K < -1.

[0028] I will now explain the significance of this configuration. Temperature drift occurs when the curved surface of a lens expands due to heat in the radial or axial direction. Of these factors, radial thermal expansion is considered to have the greatest influence on the shift in the image formation position due to temperature drift. Furthermore, this prediction is consistent with the fact that the image plane shift sensitivity per unit of power was greater at the outer edges of the lens than at the center of the lens.

[0029] If the cross-section of lens LN is a spherical lens or a similar curved surface, as exaggeratedly shown in Figure 6, the incident position of light rays on lens LN changes due to radial thermal expansion, resulting in an incident angle θ. 1α θ 2α θ1β θ 2β It changes to.

[0030] On the other hand, when the cross-section of lens LN is a conic surface such that the conic constant K < -1, the cross-section of lens LN becomes a hyperbolic surface, and as shown in Figure 7, the inclination at the outer circumference of lens LN becomes constant. That is, even if thermal expansion occurs and the incident position of the light ray changes, the inclination of the lens surface remains the same before and after thermal expansion, so the incident angle θ to the lens surface is constant. 3α =θ 3β That is the case. Although exaggerated in Figures 6 and 7, by designing the curved surface with a conic constant K < -1 to coincide with the edge 42 of the aspherical lens, the angle of incidence to the lens surface can be kept unchanged even when the incident position changes due to temperature drift, thereby reducing the change in the image formation position due to temperature drift.

[0031] Naturally, if the lens shape itself is made to approximate a conic surface similar to a triangular pyramid, as shown in Figure 7, it will not be possible to achieve the desired aberration, which defeats the purpose. Therefore, in each embodiment of the present invention described below, the central part 41 of the lens is set to an appropriate free-form surface as the base surface according to the aberration conditions, and the peripheral part 42 of the lens is set to approximate a hyperbolic surface with K < -1 as the base surface. Furthermore, in this process, the range in which "the amount of shift in the image formation position in the radial direction of the lens optical axis in response to changes in refractive power: δ becomes large," as shown in Figure 4, etc., is included in the peripheral portion 42.

[0032] These conditions are essentially equivalent to setting the conic surface so that the ray with the maximum image height is incident on the tail portion where the slope is constant. In other words, when the incident position and the distance from the lens optical axis to the ray with the maximum image height, defined by the ray matrix as shown in Figure 4, are h1, h2···hn, the approximate radius of curvature of the conic surface is R. KHowever, it is sufficient to satisfy equation (4), which states that the distance taken is even smaller than the smallest distance among h1···hn.

[0033]

number

[0034] Under these conditions, the surface to which the edge portion 42 is approximated becomes a portion of the conic surface where the slope is constant and greater than the radius of curvature. As a result, the change in the angle of incidence before and after thermal expansion is eliminated, and the effect of temperature drift can be further reduced.

[0035] Figure 8 shows an example of the cross-sectional shape of the magnifying lens for the aspherical lens LN2 that satisfies the above conditions. In the same figure, hypothetical approximation curves for the lens center 41 and edge 42 are shown so as to coincide with those portions. The image plane shift sensitivity to the corresponding TAN image plane at the lens surface is also shown so that the horizontal axis coincides with that. Note that the horizontal axis in Figure 8 represents values ​​corresponding to each position on a lens normalized as shown in Figure 5, with the lens central axis set to 0 and the effective diameter end of the lens set to 1. These values ​​do not have any particular meaning such as length. Furthermore, the change in the image formation position of the TAN image plane when the power changes by 0.0001 at each point on the lens normalized to a maximum image height of 9 mm is calculated and shown on the right vertical axis. Furthermore, the "surface shape" is defined as the line obtained by plotting the displacement of the lens surface on the left vertical axis, with the reference point at the center of the lens optical axis being (0,0). As is clear from Figure 8, the lens surface of the aspherical lens LN2 is configured such that the portion with high image plane movement sensitivity, indicated by the shaded area in Figure 8, is included in the edge portion 42.

[0036] In other words, a joint 43 is always formed between the central part 41 and the peripheral part 42 of the lens, where the two curved surfaces are joined. This joint 43 is located closer to the optical axis of the lens than the part with high sensitivity to image plane movement. This can also be seen from the fact that the intersection point of the central approximation curve, shown as a dashed line in Figure 8, and the peripheral approximation curve, shown as a dashed line, is the inflection point, which is the junction 43.

[0037] Figure 9 also shows the R2 surface, which is the reducing surface of the aspherical lens LN2. It is clear that, similar to Figure 8, the area with high image plane movement sensitivity is positioned within the edge portion 42 on the reduced side as well. Furthermore, on the reduced side, due to the complex aspherical shape, the junction between the central approximation curve and the peripheral approximation curve is widespread, resulting in a lens surface as shown in Figure 9. In this case as well, the edge portion 42 closely coincides with the hyperbolic surface which is the base surface shown as the peripheral approximation curve, and the junction portion 43 is located closer to the center of the lens optical axis than the part of the TAN image plane with high image plane movement sensitivity.

[0038] With this configuration, the projection optical system 30 of the present invention comprises a first lens group 31 having negative refractive power, a second lens group 32 having positive refractive power, and a concave mirror 39 positioned on the most magnified side of the projection optical system 30. At least one lens in the first lens group 31 is a resin aspherical lens LN2, and the cross-sectional shape of the aspherical lens LN2 has a central part 41 on the optical axis of the lens and a peripheral part 42 located on the outer periphery of the central part 41 and represented by an approximate polynomial of a hyperbolic surface, and the junction 43 of the central part 41 and the peripheral part 42 is positioned on the optical axis side of the portion of the aspherical lens LN2 with high image plane movement sensitivity. In this context, the "area with high image plane movement sensitivity" refers to the area where the image plane movement sensitivity of the central part of the lens 41 is sufficiently high, as shown by the shaded areas in Figures 8 and 9. It is thought that the appropriate value will vary depending on the performance requirements of each lens. However, if, for example, the change in the imaging position of the TAN image plane |δ| when the power fluctuation changes by 0.0001D as shown in the calculation results using the ray matrix exceeds the depth of focus, then even if the power change caused by thermal expansion is minute, it is likely to be observed as blurring on screen 104. The depth of focus is given by equation 5, and in this embodiment with an F-number of 2.2 and a scattering diameter of 5.4 μm, it is approximately 0.02376 mm. In other words, the region in which the image plane shift sensitivity becomes high enough to exceed the depth of focus shown by equation (5), as indicated by the dashed and diagonal lines in Figure 9, can be said to be the "region with high image plane shift sensitivity."

[0039]

number

[0040] Furthermore, from equation 5, if the change in image position per power 1D exceeds |δ| = 238 mm / D, it can be said that this is sufficiently high in a normal lens design, and therefore such an index value may be used. In this embodiment, the power fluctuation was set to 0.0001, resulting in the above value, but the configuration is not limited to this.

[0041] As a numerical example 1, Table 1 shows a list of the distances between the surfaces of lenses LN1 to LN17: D, radius of curvature: R, refractive index: N, and Abbe number Abv. Furthermore, Table 2 shows the conic constant K and aspheric coefficient for the enlarged (R1) and reduced (R2) sides of aspheric lens LN2, and the enlarged (R1) and reduced (R2) sides of aspheric lens LN3, respectively. Table 3 shows the conic constant K and aspheric coefficient for the enlarged (R1) and reduced (R2) sides of aspheric lens LN16.

[0042] [Table 1]

[0043] [Table 2]

[0044] [Table 3]

[0045] Furthermore, the optical performance, such as aberrations, of the projection optical system 30 using these lenses LN1 to LN17 is shown in Table 4 and Figures 10 to 14.

[0046] [Table 4]

[0047] Thus, in the numerical embodiment 1, the projection optical system 30 is a projection optical system that comprises a plurality of lenses LN1 to LN17 and magnifies and projects an image displayed on the image display surface of the image display element 102 onto the projection surface 104 as a projected image. The projection optical system 30 includes a first lens group 31 having negative refractive power, a second lens group 32 having positive refractive power, and a concave mirror 39 as a reflective member positioned on the magnification side of the projection optical system 30. Furthermore, the first lens group 31 is characterized in that at least one lens is a resin aspherical lens LN2, and the cross-sectional shape of the aspherical lens LN2 has a central part 41 on the optical axis of the lens and a peripheral part 42 located on the outer periphery of the lens central part 41 and represented by an approximate polynomial of a hyperbolic surface, and the junction 43 of the central part 41 and the peripheral part 42 is positioned on the optical axis side of the portion of the aspherical lens LN2 with high image plane movement sensitivity. With this configuration, the shape of the edge portion 42 becomes linear, so the change in the angle of incidence of light rays before and after thermal expansion is small, and the change in the image formation position on the image plane caused by temperature drift can be reduced.

[0048] Furthermore, in numerical example 1, an aspherical lens LN2 with the same shape as shown in Figures 8 and 9 is used. Therefore, as is clear from Figures 8 and 9, the bonding portion 43 is located closer to the center of the lens optical axis than the edge portion 42, and thus it is clear that the edge portion 42 does not have an inflection point.

[0049] Furthermore, in Numerical Example 1, the "high image plane shift sensitivity" refers to the range in the characteristic determinant shown in Equation 1, which is calculated from the ray matrix M of the entire projection optical system 30 and the ray matrix L of the aspherical lens LN2, where the amount of shift in the image formation position δ in the radial direction of the lens optical axis in response to a change in refractive power is shown as |δ|>238 mm / D. This is the area indicated by the shaded lines in Figure 9, and it is clear that this portion has significantly higher image plane movement sensitivity of the TAN image plane compared to the central part 41 of the lens.

[0050] Furthermore, in numerical example 1, the cross-sectional shape of the aspherical lens LN2 at the edge portion 42 is represented by an approximate polynomial of a hyperbolic surface with a conic constant K < -1. With this configuration, the edge portion 42 has a shape that closely approximates the tail portion of the hyperbolic surface, so the change in the angle of incidence of light rays before and after thermal expansion is small, and thus the change in the image formation position on the image plane caused by temperature drift can be reduced.

[0051] Furthermore, as a numerical example 2, Figure 15 shows a projection optical system 30, which is a second embodiment of the present invention. Since this embodiment is identical to the first embodiment except for the cross-sectional shape of the lens, we will omit further explanation of other components as appropriate.

[0052] Table 5 shows a list of the distances (D), radius of curvature (R), refractive index (N), and Abbe number (Abv) between the surfaces of lenses LN1 to LN17 in Numerical Example 2. Furthermore, Table 6 shows the conic constant K and aspheric coefficient for the enlarged (R1) and reduced (R2) sides of aspheric lens LN2, and the enlarged (R1) and reduced (R2) sides of aspheric lens LN3, respectively. Table 7 shows the conic constant K and aspheric coefficient for the enlarged (R1) and reduced (R2) sides of aspheric lens LN16.

[0053] [Table 5]

[0054] [Table 6]

[0055] [Table 7]

[0056] Furthermore, the optical performance, such as aberrations, of the projection optical system 30 using these lenses LN1 to LN17 is shown in Table 8 and Figures 16 to 19.

[0057] [Table 8]

[0058] In numerical example 2, the aspherical lens to which the present invention is applied is aspherical lens LN2. Figures 20 and 21 show the same diagrams for aspherical lens LN2 as in Figures 8 and 9. Similarly, Figures 22 and 23 show the same diagrams for aspherical lens LN3 as in Figures 8 and 9. As is clear from Figures 20 to 23, both the aspherical lenses LN2 and LN3 in this embodiment are formed so that their peripheral portion 42 coincides with a hyperbolic surface with a conic constant K < -1. Furthermore, in the aspherical lens LN2, the bonding portion 43 is located closer to the center of the lens optical axis than the peripheral portion 42, and at the peripheral portion 42, the lens surface shape closely matches the tail portion of the peripheral approximation curve, which is a hyperbolic surface with a conic constant K < -1, as shown by the dashed line. Therefore, it is clear that there are no inflection points at the peripheral portion 42. Furthermore, in numerical example 2, the "part with high image plane movement sensitivity" is located such that it is included in the peripheral region 42, as shown in Figures 20 and 21, using a depth of field value of 0.02376 mm as an indicator. In other words, as shown by the dashed and diagonal lines in Figure 21, the region in which the image plane shift sensitivity becomes high enough to exceed the depth of focus shown by Equation 5 can be said to be the "region with high image plane shift sensitivity," and that region is located so as to be included in the peripheral region 42.

[0059] Furthermore, as is clear from Figures 22 and 23, in numerical embodiment 2, even in the aspherical lens LN3, the bonding portion 43 is located closer to the center of the lens optical axis than the peripheral portion 42, and at the peripheral portion 42, the lens surface shape closely matches the tail portion of the peripheral approximation curve, which is a hyperbolic surface with a conic constant K < -1, as shown by the dashed line. Therefore, it is clear that there are no inflection points at the peripheral portion 42. Furthermore, in the aspherical lens LN3 of numerical example 2, the "part with high image plane movement sensitivity" is located within the peripheral portion 42, as shown in Figures 22 and 23, using a depth of field value of 0.02376 mm as an indicator. In other words, as shown by the dashed and diagonal lines in Figures 22 and 23, the region in which the image plane shift sensitivity becomes high enough to exceed the depth of focus shown by Equation 5 can be said to be the "region with high image plane shift sensitivity," and that region is located so as to be included in the peripheral region 42.

[0060] Numerical Example 3 is also shown as a comparative example of the present invention. Numerical Example 3, as shown in Figure 24, is a projection optical system in which the projection optical system 50 is composed of lenses LN1 to LN17, and a magnified image is projected toward the screen 104 by a concave mirror 39.

[0061] In Numerical Example 3 as well, it has an aspherical lens LN2 made of resin, similar to Numerical Examples 1 and 2. However, in Numerical Example 3, unlike Numerical Examples 1 and 2, although the aspherical lens LN2 approximates the edge portion 42 with a hyperbolic surface of K < -1, it is different from Numerical Examples 1 and 2 in that it does not satisfy the condition that "the radius of curvature of the approximated conic surface: R K is smaller than the smallest one among such distances: h1 ··· hn".

[0062] Table 9 shows a list of the distances: D, radii of curvature: R, refractive indices: N, and Abbe numbers Abv between the respective surfaces of lenses LN1 to LN17 in Numerical Example 3. Table 10 shows the conic constants K and aspherical coefficients of the enlarged (R1) side surface and reduced (R2) side surface of the aspherical lens LN2, the enlarged (R1) side surface and reduced (R2) side surface of the aspherical lens LN3, respectively, and Table 11 shows the conic constants K and aspherical coefficients of the enlarged (R1) side surface and reduced (R2) side surface of the aspherical lens LN16.

[0063]

Table 9

[0064]

Table 10

[0065]

Table 11

[0066] Also, the optical performances such as the aberrations of the projection optical system 50 using these lenses LN1 to LN17 are shown in Table 12 and FIGS. 25 to 29.

[0067]

Table 12

[0068] Furthermore, Figure 30 shows the reducing side (R2) of the aspherical lens LN2 in numerical practical example 3, and Figure 31 shows the expanding side (R1) of the aspherical lens LN3. As is clear from Figure 30, if the conditions of equation (4) are not met, the radius of curvature R of the conic surface K As a result of this increase, the "high image plane movement sensitivity" area, indicated by the diagonal lines, partially overlaps with the joint 43. Under these conditions, even when the edge region 42 is represented by an approximate polynomial of a hyperbolic surface with a conic constant K < -1, it became clear that the effect of temperature drift becomes relatively large, as shown in Table 13 and described later. This is the radius of curvature R of the conic surface. K When the curvature is large, the distance to the tail portion increases due to the curvature, which is thought to be why the effect of suppressing changes in the angle of incidence due to thermal expansion by making the tail portion of the hyperbolic surface and the edge portion 42 coincide well does not function sufficiently.

[0069] Table 13 summarizes the numerical values ​​for the aspherical lens LN2 in Examples 1-3. As is clear from Table 13, the aspherical lens LN2 of the present invention satisfies the condition of conic constant K < -1 and the condition shown in equation (4), so that the edge portion 42 corresponds to a portion where the slope of the hyperbolic surface is more constant, thereby reducing the effect of temperature drift.

[0070] [Table 13]

[0071] The embodiments of the present invention are as follows. [1] The projection optical system 30 of the present invention is a projection optical system that comprises a plurality of lenses LN1 to LN17 and magnifies and projects an image displayed on the image display surface of the image display element 102 onto the projection surface 104 as a projected image, and the projection optical system 30 comprises a first lens group 31 having negative refractive power, a second lens group 32 having positive refractive power, and a reflective member 39 positioned on the magnification side of the projection optical system 30. Furthermore, the first lens group 31 is characterized in that at least one lens is a resin aspherical lens LN2, and the cross-sectional shape of the aspherical lens LN2 has a central part 41 on the optical axis of the lens and a peripheral part 42 located on the outer periphery of the lens central part 41 and represented by an approximate polynomial of a hyperbolic surface, and the junction 43 of the central part 41 and the peripheral part 42 is positioned on the optical axis side of the portion of the aspherical lens LN2 with high image plane movement sensitivity. With this configuration, by making some of the lenses constituting the projection optical system less susceptible to deformation due to temperature, it is possible to achieve both low transistor (Tr) and reduced temperature drift.

[0072] [2] The projection optical system 30 of the present invention is a projection optical system described in [1], characterized in that the edge portion does not have an inflection point. With this configuration, by making some of the lenses constituting the projection optical system less susceptible to deformation due to temperature, it is possible to achieve both low transistor (Tr) and reduced temperature drift.

[0073] [3] In addition to the configurations described in [1] or [2], the portion of the aspherical lens LN2 with high image plane shift sensitivity is characterized in that, in the characteristic determinant calculated from the ray matrix of the entire projection optical system 30 and the ray matrix of the aspherical lens LN2, the amount of shift in the image formation position in the radial direction of the lens optical axis in response to a change in refractive power: δ is in the range where |δ|>238mm / D. With this configuration, by creating a shape that is less susceptible to the effects of temperature-induced deformation in areas where the image formation position in the radial direction of the lens optical axis is significantly shifted, which is prone to changes in the image plane due to temperature drift, it is possible to achieve both low transistor and reduced temperature drift.

[0074] [4] In addition to any of the configurations described in [1] to [3], the projection optical system 30 is characterized in that the cross-sectional shape of the aspherical lens at the edge portion 42 is represented by an approximate polynomial of a hyperbolic surface with a conic constant K < -1. With this configuration, by making some of the lenses constituting the projection optical system less susceptible to deformation due to temperature, it is possible to achieve both low transistor (Tr) and reduced temperature drift.

[0075] [5] In addition to the configuration described in any of [1] to [4], the projection optical system 30 of the present invention has a radius of curvature of the conic surface: R, which approximates the cross-sectional shape of the aspherical lens at the edge portion 42. K The distance between the incident point and the optical axis of the lens for the light ray that is closest to the lens optical axis among the light rays that occur on the aspherical lens and produce the maximum image height is h. min When |R K | <h min It is characterized by satisfying the following conditions. With this configuration, the surface to which the edge portion 42 is approximated becomes a portion of the conic surface that is greater than the radius of curvature and has a constant slope. As a result, the change in the angle of incidence before and after thermal expansion is eliminated, and the effect of temperature drift can be further reduced.

[0076] [6] The present invention is characterized by being an image projection device comprising a projection optical system having the configuration described in any of [1] to [5], a light source, and an image display element. With this configuration, by making some of the lenses constituting the projection optical system less susceptible to deformation due to temperature, it is possible to achieve both low transistor (Tr) and reduced temperature drift.

[0077] [7] The present invention also relates to an optical system comprising a plurality of lenses, wherein the optical system comprises a first lens group having negative refractive power and a second lens group having positive refractive power, wherein at least one lens in the first lens group is a resin aspherical lens, and the cross-sectional shape of the aspherical lens comprises a central part of the lens optical axis and a peripheral part located on the outer periphery of the central part and represented by an approximate polynomial of a hyperbolic surface, and the junction of the central part and the peripheral part is positioned on the lens optical axis side of the portion of the aspherical lens with high image plane movement sensitivity. With this configuration, by making some of the lenses constituting the optical system a shape that is less susceptible to deformation due to temperature, it is possible to achieve both low transistor (TR) and reduced temperature drift.

[0078] Although preferred embodiments of the present invention have been described above, the present invention is not limited to these specific embodiments, and various modifications and changes are possible within the scope of the spirit of the invention as described in the claims, unless otherwise specifically limited in the above description. For example, the lens unit shown in Figure 2 may be used for purposes other than projection optics. The effects described in the embodiments of the present invention are merely illustrative of the most preferred effects that may arise from the present invention, and the effects of the present invention are not limited to those described in the embodiments. [Explanation of Symbols]

[0079] 30...Projection optical system 31…First lens group 32…Second lens group 39…Concave mirror (reflective material) 41…Lens center (center) 42... Peripheral area 43…Joint part 102...Image display element (image display surface) 104...Screen (projection surface) h min ...the distance between the incident point at maximum image height and the lens optical axis. K... Conic constant LN1~LN17...Lens LN2…Aspherical lens M...ray matrix O...Lens optical axis R K ...radius of curvature of the conic surface δ... Amount of displacement [Prior art documents] [Patent Documents]

[0080] [Patent Document 1] Patent No. 5632782 [Patent Document 2] Patent No. 3921160 [Patent Document 3] Patent No. 4016576

Claims

1. Equipped with multiple lenses, A projection optical system that enlarges and projects an image displayed on the image display surface of an image display element onto a projection surface as a projected image, The projection optical system comprises a first lens group having negative refractive power, a second lens group having positive refractive power, and a reflective member positioned on the magnifying side of the projection optical system. Of the first lens group, at least one lens is an aspherical lens made of resin, The cross-sectional shape of the aspherical lens has a central part of the lens optical axis and a peripheral part located on the outer periphery of the central part that is represented by an approximate polynomial of a hyperbolic surface. The projection optical system is characterized in that the junction between the central part and the peripheral part is positioned closer to the optical axis of the lens than the part of the aspherical lens in which the image plane movement sensitivity is high.

2. A projection optical system according to claim 1, A projection optical system characterized in that the aforementioned edge portion does not have an inflection point.

3. A projection optical system according to claim 1, The region with high image plane shift sensitivity is characterized in that, in the characteristic determinant calculated from the ray matrix of the entire projection optical system and the ray matrix of the aspherical lens, the amount of shift of the image formation position in the radial direction of the lens optical axis in response to a change in refractive power, δ, is in the range where |δ| > 238 mm / D.

4. A projection optical system according to claim 1, The projection optical system is characterized in that the cross-sectional shape of the aspherical lens at the edge portion can be represented by an approximate polynomial of a hyperbolic surface with a conic constant K < -1.

5. A projection optical system according to claim 4, The radius of curvature of the conic surface that approximates the cross-sectional shape of the aspherical lens at the aforementioned edge: R Ｋ The distance between the incident position of the light ray that is closest to the lens optical axis among the light rays that occur on the aspherical lens and that produce the maximum image height, and the lens optical axis, is h. ｍｉｎ In that case, | R Ｋ | <h ｍｉｎ A projection optical system characterized by satisfying the following conditions.

6. An image projection device comprising a projection optical system according to any one of claims 1 to 5, a light source, and an image display element.

7. An optical system comprising multiple lenses, The optical system comprises a first lens group having negative refractive power and a second lens group having positive refractive power. Of the first lens group, at least one lens is an aspherical lens made of resin, The cross-sectional shape of the aspherical lens has a central part of the lens optical axis and a peripheral part located on the outer periphery of the central part that is represented by an approximate polynomial of a hyperbolic surface. The optical system is characterized in that the junction between the central part and the peripheral part is positioned closer to the optical axis of the lens than the part of the aspherical lens in which the image plane movement sensitivity is high.

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