公开(公告)号：US07301615B2

公开(公告)日：2007-11-27

申请号：US11627125

申请日：2007-01-25

申请人： Youzou Fukagawa ,  Toshiyuki Yoshihara ,  Mario Nakamori ,  Yuji Shinano

发明人： Youzou Fukagawa ,  Toshiyuki Yoshihara ,  Mario Nakamori ,  Yuji Shinano

IPC分类号： G01B9/00

CPC分类号： G03F7/706 ,  G02B7/005 ,  G02B27/0068 ,  G03F7/70258

摘要： An optical apparatus which includes an image forming optical system having a movable optical element, and a driving mechanism configured to move the optical element. The apparatus includes a first block which measures a wavefront aberration of the optical system. A second block obtains a linear evaluation value of an aberration expressed by a linear function of a position of the movable optical element out of aberrations of the optical system, and a quadratic evaluation value of a square of a root mean square of the wavefront aberration measured by the first block expressed by a quadratic function of the position. A third block uses a dummy variable as an upper limit value of the linear evaluation value and obtains a minimum value of the dummy variable by a linear programming. A fourth block determines a position of the optical element to be moved by the driving mechanism.

摘要翻译： 一种光学装置，包括具有可移动光学元件的成像光学系统和被配置为移动光学元件的驱动机构。 该装置包括测量光学系统的波前像差的第一块。 第二块获得由光学系统的像差中的可移动光学元件的位置的线性函数所表示的像差的线性评估值，并且测量波前像差的均方根的平方值的二次评估值 通过由位置的二次函数表示的第一块。 第三块使用虚拟变量作为线性评估值的上限值，并通过线性规划获得虚拟变量的最小值。 第四块确定由驱动机构移动的光学元件的位置。

公开(公告)号：US07230692B2

公开(公告)日：2007-06-12

申请号：US11080407

申请日：2005-03-16

申请人： Youzou Fukagawa ,  Toshiyuki Yoshihara ,  Mario Nakamori ,  Yuji Shinano

发明人： Youzou Fukagawa ,  Toshiyuki Yoshihara ,  Mario Nakamori ,  Yuji Shinano

IPC分类号： G01B9/00

CPC分类号： G03F7/706 ,  G02B7/005 ,  G02B27/0068 ,  G03F7/70258

摘要： An optical apparatus including an image forming optical system having a movable optical element, and a driving mechanism. A first block obtains a linear evaluation value by normalizing, by a first tolerance, an aberration expressed by a linear function of a position of the movable optical element and normalizing, by a second tolerance, an aberration expressed by a quadratic function of the position out of the aberrations of the optical system. A second block obtains a minimum value of a dummy variable by linear programming. A third block determines a position of the optical element to be moved by the driving mechanism using a value prepared by adding a relaxation amount to the minimum value obtained by the second block and minimizes the weighted sum of the quadratic evaluation values by adjusting the weights assigned to the quadratic evaluation values and a relaxation amount.

摘要翻译： 一种包括具有可移动光学元件的成像光学系统和驱动机构的光学装置。 第一块通过以第一公差标准化由可移动光学元件的位置的线性函数表示的像差并且归一化第二公差来获得线性评估值，由位置输出的二次函数表示的像差 的光学系统的像差。 第二个块通过线性规划获得虚拟变量的最小值。 第三块通过使用通过将松弛量添加到由第二块获得的最小值来准备的值来确定由驱动机构移动的光学元件的位置，并且通过调整分配的权重来最小化二次评估值的加权和 到二次评价值和松弛量。

公开(公告)号：US20050206880A1

公开(公告)日：2005-09-22

申请号：US11080407

申请日：2005-03-16

申请人： Youzou Fukugawa ,  Toshiyuki Yoshihara ,  Mario Nakamori ,  Yuji Shinano

发明人： Youzou Fukugawa ,  Toshiyuki Yoshihara ,  Mario Nakamori ,  Yuji Shinano

IPC分类号： G03F7/20 ,  G01B9/00 ,  G02B7/00 ,  G02B27/00 ,  H01L21/027

CPC分类号： G03F7/706 ,  G02B7/005 ,  G02B27/0068 ,  G03F7/70258

摘要： An optical apparatus including an image forming optical system having a movable optical element, and a driving mechanism which moves the optical element is disclosed. The apparatus comprises a first block which obtains a linear evaluation value by normalizing, by a first tolerance, an aberration expressed by a linear function of a position of the movable optical element out of aberrations of the optical system, and a quadratic evaluation value by normalizing, by a second tolerance, an aberration expressed by a quadratic function of the position out of the aberrations of the optical system, a second block which obtains a minimum value of a dummy variable by linear programming using an upper limit value of the linear evaluation value as the dummy variable, and a third block which determines a position of the optical element to be moved by the driving mechanism so as to minimize a weighted sum of the quadratic evaluation values with respect to a plurality of image heights by using, as the upper limit value of the linear evaluation value, a value prepared by adding a relaxation amount to the minimum value of the dummy variable that is obtained by the second block. The third block minimizes the weighted sum of the quadratic evaluation values by adjusting the weights assigned to the quadratic evaluation values and the relaxation amount.

摘要翻译： 公开了一种包括具有可移动光学元件的成像光学系统和移动光学元件的驱动机构的光学装置。 该装置包括第一块，其通过以第一公差标准化由光学系统的像差中的可移动光学元件的位置的线性函数所表示的像差，以及通过归一化归一化二次评估值来获得线性评估值 通过第二公差，由光学系统的像差之外的位置的二次函数表示的像差，通过使用线性评估值的上限值通过线性规划获得虚拟变量的最小值的第二块 作为虚拟变量，以及第三块，其确定由驱动机构移动的光学元件的位置，以便通过使用作为上部的图像来最小化相对于多个图像高度的二次评估值的加权和 线性评估值的极限值，通过将松弛量与由该se获得的虚拟变量的最小值相加而制备的值 cond block。 第三块通过调整分配给二次评价值的权重和松弛量来最小化二次评价值的加权和。

公开(公告)号：US07346886B2

公开(公告)日：2008-03-18

申请号：US11103459

申请日：2005-04-12

申请人： Youzou Fukagawa ,  Mario Nakamori

发明人： Youzou Fukagawa ,  Mario Nakamori

IPC分类号： G06F17/50

CPC分类号： G06F17/5072 ,  G03F7/70433

摘要： In determining a relative position between a chip lattice including rectangular cells, each of which has a size of a chip to be formed on a substrate and an effective area on the substrate, one representative cell in the chip lattice is divided into a plurality of partial areas in accordance with an existing area, of a representative point of the effective area, in which chip sets trimmed from the chip lattice with the effective area are identical. A partial area corresponding to a chip set including a maximum number of chips is specified from the plurality of partial areas, and the representative point is set in the specified partial area.

摘要翻译： 在确定包括矩形单元的芯片格子之间的相对位置，其中每一个具有要在衬底上形成的芯片的尺寸和衬底上的有效区域时，芯片晶格中的一个代表单元被分成多个部分 根据现有区域，有效区域的代表点的区域相同，其中从芯片格子修剪的芯片组具有有效区域。 从多个部分区域指定与芯片组对应的部分区域，并且将代表点设定在指定的部分区域。

公开(公告)号：US20050253215A1

公开(公告)日：2005-11-17

申请号：US11103459

申请日：2005-04-12

申请人： Youzou Fukagawa ,  Mario Nakamori

发明人： Youzou Fukagawa ,  Mario Nakamori

IPC分类号： G03F7/20 ,  G06F17/50 ,  H01L21/027 ,  H01L31/058

CPC分类号： G06F17/5072 ,  G03F7/70433

摘要： In determining a relative position between a chip lattice comprised of rectangular cells each of which has a size of a chip to be formed on a substrate and an effective area on the substrate, one representative cell in the chip lattice is divided into a plurality of partial areas in accordance with an existing area, of a representative point of the effective area, in which chip sets trimmed from the chip lattice with the effective area are identical. A partial area corresponding to a chip set including a maximum number of chips is specified from the plurality of partial areas, and the representative point is set in the specified partial area.

摘要翻译： 在确定由矩形单元组成的芯片晶格之间的相对位置，每个矩形单元具有要在衬底上形成的芯片的尺寸和衬底上的有效区域，芯片晶格中的一个代表单元被分成多个部分 根据现有区域，有效区域的代表点的区域相同，其中从芯片格子修剪的芯片组具有有效区域。 从多个部分区域指定与芯片组对应的部分区域，并且将代表点设定在指定的部分区域。

公开(公告)号：US20070115458A1

公开(公告)日：2007-05-24

申请号：US11627125

申请日：2007-01-25

申请人： Youzou Fukagawa ,  Toshiyuki Yoshihara ,  Mario Nakamori ,  Yuji Shinano

发明人： Youzou Fukagawa ,  Toshiyuki Yoshihara ,  Mario Nakamori ,  Yuji Shinano

IPC分类号： G01B9/00

CPC分类号： G03F7/706 ,  G02B7/005 ,  G02B27/0068 ,  G03F7/70258

摘要： An optical apparatus including an image forming optical system having a movable optical element, and a driving mechanism which moves the optical element is disclosed. The apparatus comprises a first block which obtains a linear evaluation value by normalizing, by a first tolerance, an aberration expressed by a linear function of a position of the movable optical element out of aberrations of the optical system, and a quadratic evaluation value by normalizing, by a second tolerance, an aberration expressed by a quadratic function of the position out of the aberrations of the optical system, a second block which obtains a minimum value of a dummy variable by linear programming using an upper limit value of the linear evaluation value as the dummy variable, and a third block which determines a position of the optical element to be moved by the driving mechanism so as to minimize a weighted sum of the quadratic evaluation values with respect to a plurality of image heights by using, as the upper limit value of the linear evaluation value, a value prepared by adding a relaxation amount to the minimum value of the dummy variable that is obtained by the second block. The third block minimizes the weighted sum of the quadratic evaluation values by adjusting the weights assigned to the quadratic evaluation values and the relaxation amount.

摘要翻译： 公开了一种包括具有可移动光学元件的成像光学系统和移动光学元件的驱动机构的光学装置。 该装置包括第一块，其通过以第一公差标准化由光学系统的像差中的可移动光学元件的位置的线性函数所表示的像差，以及通过归一化归一化二次评估值来获得线性评估值 通过第二公差，由光学系统的像差之外的位置的二次函数表示的像差，通过使用线性评估值的上限值通过线性规划获得虚拟变量的最小值的第二块 作为虚拟变量，以及第三块，其确定由驱动机构移动的光学元件的位置，以便通过使用作为上部的图像来最小化相对于多个图像高度的二次评估值的加权和 线性评估值的极限值，通过将松弛量与由该se获得的虚拟变量的最小值相加而制备的值 cond block。 第三块通过调整分配给二次评价值的权重和松弛量来最小化二次评价值的加权和。