System Matrix for a Thick Lens

厚透镜的系统矩阵

This is an examination of the system matrix for a thick lens in the form used by Meyer-Arendt. An alternative form of the system matrix is used by Hecht.

这是Meyer-Arendt所采用的厚透镜系统矩阵的考察。Hecht采用了一种不同的系统矩阵形式。

The example is for a lens with index of refraction n surrounded by air (n=1). It involves the surface powers of the lens and the thickness d between the vertexes. It also involves the principal planes H₁ and H₂. As with most ordinary geometrical optics, it is applicable only for small angles (paraxial rays). The development also follows the cartesian sign convention.

For glass with index of refraction
n_lens = n =

对于折射率为n的透镜，有n =

中文译文中的待填/计算数值依次对应：1：n。实际数值以上方原输入框为准。

the front surface power for lens radius
R₁ = m is P₁ = m^-1

透镜半径 R₁ 的前表面功率为 m 时，P₁ = m - 1

中文译文中的待填/计算数值依次对应：1：r1 2：p1。实际数值以上方原输入框为准。

and the back surface power for lens radius
R₂ = m is P₂ = m^-1

以及透镜半径R₂ = m时的后表面功率P₂ = m - 1

中文译文中的待填/计算数值依次对应：1：r2 2：p2。实际数值以上方原输入框为准。

Lens thickness d = m

(Note that for a double convex lens, the front surface radius R₁ is positive and the back surface radius R₂ is negative according to the Cartesian sign convention.)

（注意，对于双凸透镜，根据笛卡尔符号约定，前表面半径R1为正，后表面半径R2为负。）

透镜的厚度 d = m

中文译文中的待填/计算数值依次对应：1：d。实际数值以上方原输入框为准。

The symbols used by Meyer-Arendt for the elements of the system matrix will be used.

b =	a =
d =	c =

梅耶-阿伦特用于系统矩阵元素的符号将被使用。

中文译文中的待填/计算数值依次对应：1：mb 2：ma 3：md 4：mc。实际数值以上方原输入框为准。

A number of other characteristics of the thick lens may be calculated from the system matrix.

厚透镜的许多其他特性可以从系统矩阵中计算出来。

The right-hand, or equivalent focal length of the lens is just the reciprocal of matrix element a: f₂ = 1/a = m.

透镜的右手法则，或等效焦距，就是矩阵元素a的倒数：f₂ = 1/a = m。

中文译文中的待填/计算数值依次对应：1：f2。实际数值以上方原输入框为准。

The distance V₂H₂ from the right vertex to the associated principal plane is given by V₂H₂= (c-1)/a = m.

从右顶点到相关主平面的距离V₂H₂由V₂H₂ = (c-1)/a = m给出。

中文译文中的待填/计算数值依次对应：1：v2h2。实际数值以上方原输入框为准。

The right vertex focal length (or back focal length) is given by f_v2 = c/a = m.

右顶点焦距（或后焦距）由 f v2 = c/a = m 给出。

中文译文中的待填/计算数值依次对应：1：fv2。实际数值以上方原输入框为准。

Note that the equivalent focal length f₂ is the sum of the back vertex focal length and the distance from the vertex to the principal plane: f₂ = f_v2 + V₂H₂. Similar relationships exist for the left-hand or front vertex.

注意，等效焦距 f₂ 是后顶点焦距与顶点到主平面距离之和：f₂ = f_v2 + V₂ H₂。类似的关系也适用于左顶点或前顶点。

The left vertex focal length (or front focal length) is given by f_v1 = -b/a = m.

左顶点焦距（或前焦距）由 f_v1 = -b/a = m 给出。

中文译文中的待填/计算数值依次对应：1：fv1。实际数值以上方原输入框为准。

The distance V₁H₁ from the left vertex to the associated principal plane is given by V₁H₁= (1-b)/a = m.

从左顶点到相关主平面的距离V₁H₁由V₁H₁ = (1 - b)/a = m给出。

中文译文中的待填/计算数值依次对应：1：v1h1。实际数值以上方原输入框为准。

The equivalent front focal length f₁ is then given by f₁ = -(b/a + V₁H₁) = m.

等效前焦点焦距 f₁ 则由 f₁ = -(b/a + V₁ H₁ ) = m 给出。

中文译文中的待填/计算数值依次对应：1：f1。实际数值以上方原输入框为准。

Image location for thick lens from system matrix

厚透镜系统矩阵像距