201211587 六、發明說明： 【發明所屬之技術領域】 鏡 本發明係與光學鏡片有關，特別是關於-種非球面 片之設計方法。 【先前技術】 目前市面上所販售之光學讀寫頭、相機鏡頭、眼鏡與 隱形眼鏡等產品已大量採用非球面鏡片，其中，傳統隱形 眼鏡為了兼顧屈光度的精確度與使用者配戴的舒適性，所 f用非球面鏡片的外側鏡面是以其中心點向外採取多段曲 =進行設計，使外側鏡面呈現不連續的之曲面，雖然鏡 :心區域的光學區内屈光度符合鏡片設計上的要求，作 觀卜觀上卻存在有同心圓的現象，並不能符合鏡片外 =透明的要求’且容易造成使用者配麟的異物感。 2，狩㈣料透㈣線擬合(CufveFitting)以設 芯2曲面取代原本多段轉_設計，—般是應用 續曲二== 式:藉由數學方法來得到較佳的連 數越古，^ 進行曲線擬合，多項式的次方 導致連續曲面與多段曲率之产二一疋最後一項吊數項往往 量，造柄細麵效果不t雜處產生過大的誤差 進行::擬:業=Γ以一般偶次項的非球面方程式 但是所擬合得到的連心用多項式方程式之缺失， 的連、，只曲面與多段曲率鏡面在光學區内的 201211587 擬合誤差值仍大，亟需進一步改善 【發明内容】 >有鑑於此，本發明之目的在於提供一種非球面鏡片之 設計方法’其能有效降㈣線擬合所得到連續曲 的光學區内的擬合誤差值。 為達上揭之目的’本發明所提供非球面鏡片之 法，其包含下列步驟：a.提供一非球面鏡片，具有Γ凹向 内之第-鏡面、—凸向外的第二鏡面、以及—位於該鏡片 中心區域之光學區，其中該第二鏡面 一以今楚-锫而由田…多奴曲率’ b.設定 以該第-鏡面中心點為原點之(χ，γ)座標系統， 軸為該第二鏡面之光軸，以固定乂方向之增量，量測 :鏡=上複數個座標點；e期—非球面方程式，辭 =步驟所得的座標點針對該第二鏡面進行曲線擬合^ 么武如下· 式令，Z表示γ方向與座標原 面鏡片中心曲率，r表干γ 士人t 雕C衣不非球 * _ . '、X方向與座標原點的距離，％ 表不r各階項次的係數； ％〜8 求解該非球面方程式中⑹， 繪製的-曲面，使該曲麟 1_非珠面株式所 差值為最小。 …綠—鏡秘該光學區内的擬合誤 經由上述步驟，俾可寐 ΛΑ Λ . 早了獲仔一符合鏡片屈光度及透明外 201211587 ，要求之非球顿片，且鏡片鮮區_合誤差值將有效 地降被。 【實施方式】 為了更…解本發明之特點所在，兹舉以下一較佳非球 面鏡片之料方法並配合圖式說明如下，其中： 第圖係本發明一較佳設計方法之流程圖； 第二圖係本發明_面鏡#示意圖； 第三圖係本發明第一實施例曲線擬合之曲線圖； 第四圖係本發明第一實施例曲線擬合誤差值隨半徑之 變化圖； 第五圖係本發明第二實施例曲線擬合之曲線圖；以及 第六圖係本發明第二實施例曲線擬合誤差值隨半徑之 變化圖。 >請參閱第-圖及第二圖，本發明提供一非球面鏡片之 设計方法係包含下列步驟： 第-步驟s卜提供—非球面鏡片1G，其具有一凹向内 =第-鏡面1卜-凸向外的第二鏡面12、以及—位於該鏡片 中心區域之光學區13 ’其中該第-鏡面U為單—曲率，該 第二鏡面12自其中心區域向外分別設為多段曲率。 第-步驟S2 ’ 4 —以該第二鏡面中心點為原點之 (X，Y)座標系統，其中γ軸為該第二鏡面12的光軸，進而 沿著該Χ·γ平面定義出—位於該第二鏡面12之原始曲線 12a’X表示該原始曲線12a上任一點至¥轴的垂直高度， 5 201211587 並藉由固定x方向之增量為_lmm，量測該原始曲線仏 上複數個座標點。 第三步驟S3，採用一非球面方程式，藉由前述步驟所 得的複數個座標點，針對該原始曲線12a進行曲線擬合， 該公式如下： 口 + ν6 + a4r& + a/0+a6rn …3，τγ 十《厂切6^+α/4+ν16 α3~8 式中，ζ表示Υ方向與座標原點的距離，c表示非球 面鏡片中心曲率，r表示X方向與座標原點的距離， 表示r各階項次的係數 將第二步驟S2戶斤量測到之所有座標點，代入該非球面 方程式，求解至少-組轉球面絲式之各階係數值，再 以-最小平方法選取該非球Φ方料崎製的—曲線使 該曲線與該原始曲線12a於該光學區13内的擬合誤差值為 最小。 ' … -般隱形眼鏡鏡片之鏡面可分為中心區域的光學區及 外圍區域的非光學區，-般成人眼睛瞳孔尺寸大小約 3〜4mm’考量視角之後，光學區可定義為以鏡面中心為圓 心且直徑5mm的圓形區域。於光學區内，該非球面方程式 所繪製之曲線與該第二鏡面丨2之原始曲線丨2 a間的擬合誤 差值必須精確配合該第二鏡面12之屈光度，至於非光學區 内，僅涉及使用者配戴的舒適感，與光學區相較之下，可 容許較大之擬合誤差值。 為具體說明本發明所提供設計方法之功效，以下所舉 201211587 實施例係利用上述之步驟設計一屈光度為_ 5. G D之隱形眼 鏡的鏡片為例，為了比較使用不同非球面方程式進行曲線 擬合後所得之求解曲線與該第二鏡面12之原始曲線12a 間的擬合誤差值’因此’第—實施例是採用習知偶次項非 球面方程以作為對照實驗，而第二實施_是採用木 明所提供的非球面方程式。 λ 如下列公 第一實施例所採用一偶次項非球面方程式， 式所示： Ζ cr2 式中，可分成圓錐部份項a及非球面項b兩部分，z 表示Y方向與座標原點的距離，e表示非球面鏡心: 率’ r表示X方向與座標原點的距離，k為圓錐係數，^ 表示r各階項次的係數。 αι〜8 以該偶次項非球面方程式與該第二_ 12之原始 f以進行曲線擬合，其結果如第三_示，從光學^半 徑〇.12mm處至非光學區半徑6 71mm處，該方程式之 曲線與該原始曲線12a的曲線擬合效果不錯。另外，擬人 誤差值分析結果如第四圖所示，光學 ° 最大擬合誤差值為5卿。 ~1·6ηπη處之 本發明所提供第二實施例則改採用發明人多 後修正之非球•喊，其修正之部分_其_部分項 201211587 的分子設定為l，且令圓錐係數k值設定為〇,非球面項之 二次項至八次項的係數值設定為〇，修正後之公式如下： z = 2 + a5r10 + a/2 + a7ru + a/b 其曲線擬合與擬合誤差值分析結果分別如第五圖及第 六圖所示’修正後之非球面方程式的求解曲線與該第二鏡 面12的原始曲線具有相當好曲線擬合之效果，於光學區 内’擬合誤差值為〇μιη，而非光學區的最大誤差值係約 15μιη ’並不影響使用者佩戴的舒適感。 比較前述二實施例於光學區内之擬合誤差值，如第四 圖與第六圖所示，比對兩圖中於光學區半徑2 5mm内所表 現之最大擬合誤差值’很明顯地看出採用修正後非球面方 私式進行曲線擬合的第二實施例已能有效地降低採用一般 非球面方程式進行曲線擬合的第一實施例於光學區内之最 大擬合誤差值。 在此說明的是，本發明所採用的非球面方程式六次項 與八次項⑽數值亦可不設定為G，其曲線擬合的效果亦 佳。 綜合上述數據顯示，採用修正後非球面方程式對該第 進行祕擬合，残轉出—最佳㈣連續曲面 以取代原本多段曲率而非連續的第二鏡面12，且完 於光學區内屈光度及整體透明外^ " 配戴的舒適性。 卜觀之要P並兼顧使用者 201211587 【圖式簡單說明】 第一圖係本發明一較佳設計方法之流程圖； 第二圖係本發明非球面鏡片示意圖； 第三圖係本發明第一實施例曲線擬合之曲線圖； 第四圖係本發明第一實施例曲線擬合誤差值隨半徑之 變化圖； 第五圖係本發明第二實施例曲線擬合之曲線圖；以及 第六圖係本發明第二實施例曲線擬合誤差值隨半徑之 變化圖。 12第二鏡面 13光學區 S2 :第二步驟201211587 VI. DESCRIPTION OF THE INVENTION: TECHNICAL FIELD OF THE INVENTION The present invention relates to optical lenses, and more particularly to a method for designing aspherical sheets. [Prior Art] At present, aspherical lenses have been widely used in optical pickups, camera lenses, glasses and contact lenses sold on the market. Among them, traditional contact lenses are designed to balance the accuracy of diopter with the comfort of users. Sexuality, the outer mirror surface of the aspherical lens is designed to adopt a multi-segment of the center point to make the outer mirror surface appear discontinuous, although the mirror: the optical area of the heart region conforms to the lens design. It is required that there is a phenomenon of concentric circles on the viewpoint of observation, and it cannot meet the requirements of the outside of the lens = transparency, and it is easy to cause the foreign body sensation of the user. 2, hunting (four) material through (four) line fitting (CufveFitting) to replace the original multi-segment rotation with the design of the core 2 surface, the general application of the second song ==: by mathematical methods to obtain a better number of times, ^ Performing curve fitting, the power of the polynomial leads to the production of continuous surface and multi-segment curvature. The last item of the number of hangs is often quantity, and the effect of the fine surface of the shank is not excessively mixed: #拟:业=Γ In the case of the aspherical equation of the general even term, but the fitting of the missing polynomial equation, the fitting error of the 201211587 in the optical zone of the continuous curved surface and the multi-section curvature mirror is still large, and further improvement is needed. SUMMARY OF THE INVENTION In view of the above, an object of the present invention is to provide a method for designing an aspherical lens which can effectively reduce the fitting error value of the continuous curved optical region obtained by the (four) line fitting. The method for providing an aspherical lens according to the present invention includes the following steps: a. providing an aspherical lens having a first-mirror surface that is concave inward, a second mirror surface that is convex outward, and - an optical zone located in a central region of the lens, wherein the second mirror surface is a χ γ 曲率 由 由 由 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多 多The axis is the optical axis of the second mirror, measured in the increment of the fixed 乂 direction, and the measurement: the mirror = the upper plurality of coordinate points; the e period - the aspheric equation, the speech point obtained by the step = the curve of the second mirror Fitting ^ 武武 is as follows: 式, Z is the γ direction and the center curvature of the original lens of the coordinate, r is dry γ 士士人 t 雕 C clothing is not the ball * _ . ', the distance between the X direction and the coordinate origin, % The coefficient of each order of the r-th order is calculated; %~8 solves the (6) in the aspheric equation, and the drawn-surface is such that the difference of the Qulin 1_ non-bead pattern is the smallest. ... Green - Mirror Secret The fitting in the optical zone is incorrectly passed through the above steps, and it can be used as early as the lens is in accordance with the lens diopter and transparent 201211587, the required non-ball sheet, and the lens fresh zone _ error The value will be effectively reduced. [Embodiment] In order to further explain the features of the present invention, the following preferred method for aspherical lens is described below with reference to the drawings, wherein: Figure 1 is a flow chart of a preferred design method of the present invention; 2 is a schematic diagram of the present invention _ face mirror; the third figure is a curve of the curve fitting of the first embodiment of the present invention; the fourth figure is a graph of the curve fitting error value with the radius of the first embodiment of the present invention; The fifth graph is a graph of curve fitting of the second embodiment of the present invention; and the sixth graph is a graph of the curve fitting error value as a function of radius according to the second embodiment of the present invention. > Referring to the first and second figures, the present invention provides a method for designing an aspherical lens comprising the following steps: Step-by-step providing - aspherical lens 1G having a concave inward = first-mirror a second convex surface 12, and an optical zone 13' located in a central region of the lens, wherein the first mirror surface U is a single curvature, and the second mirror surface 12 is respectively divided into a plurality of segments from a central region thereof Curvature. Step-S2 '4 - an (X, Y) coordinate system with the second mirror center point as the origin, wherein the γ-axis is the optical axis of the second mirror 12, and then defined along the Χ·γ plane - The original curve 12a'X located at the second mirror 12 indicates the vertical height from any point on the original curve 12a to the axis, 5 201211587, and the original curve is measured by the fixed x direction increment of _lmm. Coordinate point. In the third step S3, an aspherical equation is used to perform curve fitting on the original curve 12a by using a plurality of coordinate points obtained in the foregoing steps. The formula is as follows: Port + ν6 + a4r& + a/0+a6rn ... 3 , τγ 十 “Factory cut 6^+α/4+ν16 α3~8 where ζ represents the distance between the Υ direction and the coordinate origin, c represents the central curvature of the aspherical lens, and r represents the distance between the X direction and the coordinate origin. The coefficient indicating the order of each step of r is all the coordinate points measured by the second step S2, and is substituted into the aspheric equation to solve the coefficient values of the at least one set of the spherical surface, and then the non-spherical Φ is selected by the least square method. The squared-curve curve minimizes the fitting error value of the curve and the original curve 12a in the optical zone 13. The mirror surface of the general contact lens can be divided into the optical zone of the central area and the non-optical zone of the peripheral zone. The size of the pupil of the adult eye is about 3~4mm. After considering the angle of view, the optical zone can be defined as the center of the mirror. A circular area with a center and a diameter of 5 mm. In the optical zone, the fitting error value between the curve drawn by the aspherical equation and the original curve 丨2 a of the second mirror 丨2 must exactly match the diopter of the second mirror 12, as in the non-optical zone, only The comfort that the user wears allows for a larger fitting error value than the optical zone. To specifically illustrate the efficacy of the design method provided by the present invention, the following 201211587 embodiment uses the above steps to design a lens of a diopter having a diopter of _ 5. GD as an example, for comparison using different aspheric equations for curve fitting The fitting error value between the solution curve obtained afterwards and the original curve 12a of the second mirror 12 is 'therefore' the first embodiment uses a conventional even-order aspheric equation as a control experiment, and the second implementation _ is a wood The aspheric equation provided by Ming. λ As shown in the following first embodiment, an even-order aspherical equation is used, as shown in the formula: Ζ cr2, which can be divided into two parts: a conical part a and an aspherical item b, where z represents the Y direction and the coordinate origin. The distance, e represents the aspherical mirror core: the rate 'r denotes the distance between the X direction and the coordinate origin, k is the conic coefficient, and ^ denotes the coefficient of each order of r. Ιι~8 is curve-fitted with the even-order aspherical equation and the original _12 of the second -12, and the result is as shown in the third _, from the optical ^radius 〇.12mm to the non-optical zone radius of 6 71mm, The curve of this equation fits well with the curve of the original curve 12a. In addition, the results of the anthropomorphic error analysis are shown in the fourth figure, and the optical ° maximum fitting error value is 5 qing. The second embodiment provided by the present invention at ~1·6ηπη is changed to the aspherical shouting modified by the inventor, and the modified part _the _ part of the item 201211587 is set to l, and the conic coefficient k value Set to 〇, the coefficient value of the quadratic to eighth term of the aspheric term is set to 〇, and the modified formula is as follows: z = 2 + a5r10 + a/2 + a7ru + a/b Its curve fitting and fitting error value The analysis results are as shown in the fifth and sixth figures respectively. The corrected curve of the aspheric equation and the original curve of the second mirror 12 have a fairly good curve fitting effect, and the fitting error value in the optical zone For 〇μιη, the maximum error value of the non-optical zone is about 15 μm, which does not affect the comfort of the user. Comparing the fitting error values of the foregoing two embodiments in the optical zone, as shown in the fourth and sixth figures, comparing the maximum fitting error values expressed in the optical zone radius of 2 5 mm in both figures is clearly It is seen that the second embodiment of the curve fitting using the modified aspherical private equation has been effective in reducing the maximum fitting error value of the first embodiment in the optical zone using the general aspheric equation for curve fitting. It is explained here that the numerical values of the six-term and eight-order (10) values of the aspheric equation used in the present invention are not set to G, and the effect of curve fitting is also good. Based on the above data, the modified aspheric equation is used to fit the first part, and the best (four) continuous curved surface is replaced by the original multi-segment curvature instead of the continuous second mirror 12, and the diopter and the optical region are completed. Overall transparent outside ^ " wearing comfort.卜观之要P and user 201211587 [Simplified description of the drawings] The first figure is a flow chart of a preferred design method of the present invention; the second figure is a schematic view of the aspherical lens of the present invention; The graph of the curve fitting of the embodiment; the fourth graph is a graph of the curve fitting error value with the radius of the first embodiment of the present invention; the fifth graph is the graph of the curve fitting of the second embodiment of the present invention; The figure is a graph showing the variation of the curve fitting error value with the radius of the second embodiment of the present invention. 12 second mirror 13 optical zone S2: second step
【主要元件符號說明】 10非球面鏡片 11第一鏡面 12a原始曲線 S1 :第一步驟 S3 :第三步驟[Main component symbol description] 10 aspherical lens 11 first mirror 12a original curve S1: first step S3: third step