201222013 六、發明說明： 【發明所屬之技術頜域】 本發明係關於一種可變焦距液體透鏡的像差補償方 法’更特別是關於用以解決非固體透鏡所產生像差之像差 補償方法。 【先前技術】 在習知光學系統中’係利用透鏡對於光線的聚焦與發 散特性’藉以對待觀察物進行放大或縮小的觀察。然而， • 透鏡於觀察該待觀察物時’係存在有像差的問題，且該像 差問題係同時會影響成像的品質，其有可能發生變形或模 糊不清的現象。其中，特別是所謂的球面像差（spherical aberration)的部份，而產生該球面像差的問題係由於光線入 射至透鏡不同的位置，使得該光線經由該透鏡聚焦時並不 會聚焦於同一焦點上，而僅會產生於一焦平面上’因而產 生像差的問題。 φ 為解決上述之問題，習知技術係透過使用非球面像差 透鏡或複合透鏡的方式，用以消除該像差的產生，但該等 技術係使用於利用玻璃等透明固體所製作的透鏡上，無法 適用於非gj體之透鏡，例如液體透鏡等非固體的透鏡。 液體遷鏡為例，該液體透鏡係在透鏡中裝填液體， 使得可藉由該液體調整該透鏡之薄膜的表面曲率，用以带 成外=或内凹之透鏡。再者，該表面曲率的改變，係更佳 地使付該液體透鏡具有可變焦距或可變倍率之功能 而，由方^. “、、 、為知液體透鏡因透鏡表面的形狀難以或無法調 201222013 整，因此在中高倍率時很容易產生嚴重之球面像差問題， 進而使得成像品質不佳。 故本發明係提出一種可用以解決液體透鏡因像差問題 所造成成像品不佳的問題。 【發明内容】 本發明係提供一種可變焦距液體透鏡的像差補償方 法，其係藉由選自於該可變焦距液體透鏡之高倍率至低倍 率中所有倍率之最小球面像差之平均曲率半徑比值，再根 據所對應之第一透鏡面與第二透鏡面所對應薄膜變形量比 值或彈性係數比值之厚度比值，用以選擇適當的第一薄膜 與第二薄膜，用以達到在所有倍率下可獲得較小像差之目 的。 為達上述目的，本發明提出一種可變焦距液體透鏡的 像差補償方法，係用以補償該液體透鏡之第一透鏡面與第 二透鏡面所形成之像差，而該第一透鏡面係具有第一曲率 半徑與該第二透鏡面係具有第二曲率半徑，該方法包含： 於步驟si中，係選定該可變焦距液體透鏡的口徑、鏡身厚 度與注入該液體透鏡内液體之折射率；於步驟S2中，係在 選定該口徑、該鏡身厚度與該折射率之後設定複數透鏡倍 率之至少其一倍率，並藉以確定對應該等透鏡倍率之其一 的該第一透鏡面與該第二透鏡面之複數曲率半徑組合；於 步驟S3中，係根據已選定的該等曲率半徑組合，用以計算 對應該等曲率半徑組合之複數球面像差；於步驟S4中，係 選取該等球面像差中最小的球面像差，用以決定產生對應 201222013 最小該球面像差之該等曲率半徑組合所需的該第一 與該第二透鏡面，以產生曲率半徑比值；於步驟S5鏡面 設定該等透鏡倍率之至少另外其一，以重複執行該幻，係 S5步驟，直到獲得該可變焦距液體透鏡之所有的該至該 倍率所分別地對應的該曲率半徑比值，並根據該等曲=鏡 徑比值用以取得該可變焦距液體透鏡之平均曲率半徑= 值；於步驟S6中，係根據已選定的該平均曲率半徑比值， 計算並選取該第一透鏡面與該第二透鏡面所對應薄膜變形 鲁里比值或彈性係數比值之厚度比值；以及，於S7中，係選 擇對應該厚度比值之第一薄膜與第二薄膜，用以取代該第 一透鏡面與該第二透鏡面。 與習知技術相較’本發明係用以解決習知利用非固體 式透鏡所產生像差的問題，其中該像差問題係由於該非固 體式透鏡表面的形狀難以或無法進行調整的緣故。特別是 當該非固體式透鏡在高倍率使用時，更會產生嚴重之球面 馨 像差問題，而該球面像差問題勢必會影響非固體式透鏡的 成像品質。然而’藉由本發明所提出之像差補償方法，其 係可確實地達成可在所有倍率下可獲得較小像差之目的。 此外，本發明係可藉由模擬與實際的操作下驗證在所 有倍率下可獲得較小像差。 【實施方式】 為充分瞭解本發明之目的、特徵及功效，茲藉由下述 具體之實施例，並配合所附之圖式，對本發明做一詳細說 明，說明如後： 201222013 同時參考第1圖與第2圖，係本發明之可變焦距液體 透鏡的像差補償方法之示意圖與流程圖。於第1圖中，可 變焦距液體透鏡的像差補償方法係用以補償該液體透鏡2 之第一透鏡面22與第二透鏡面24所形成的像差S(亦即 |FP-FM|)，其中，該第一透鏡面22係具有第一曲率半徑q 與該第二透鏡面24係具有第二曲率半徑r2。 於第2圖中，可變焦距液體透鏡的像差補償方法係包 含：起始於步驟S1，係選定該可變焦距液體透鏡2的口徑 A、鏡身厚度d與注入該液體透鏡内液體4之折射率η。 接著步驟S2，係在選定該口徑、該鏡身厚度與該折射 率之後設定複數透鏡倍率之至少其一倍率，並藉以確定對 應該等透鏡倍率之其一的該第一透鏡面與該第二透鏡面之 複數曲率半徑組合。 接著步驟S3，係根據已選定的該等曲率半徑組合，用 以計算對應該等曲率半徑組合之複數球面像差；再接著步 驟S4，係選取該等球面像差中最小的球面像差，用以決定 對應產生最小該球面像差之該等曲率半徑組合所需的該第 一透鏡面與該第二透鏡面，以產生曲率半徑比值。 接著步驟S5，係設定該等透鏡倍率之至少另外其一， 以重複執行該S2至該S5步驟，直到獲得該可變焦距液體 透鏡之所有的該等透鏡倍率所分別地對應的該曲率半徑比 值，並根據該等曲率半徑比值用以取得該可變焦距液體透 鏡之平均曲率半徑比值。 步驟S6，係根據已選定的該平均曲率半徑比值，計算 201222013 選取該第一透鏡面與該第二透鏡面所對應之薄膜變形量比 值或薄膜彈性係數比值之的厚度比值；以及，於步驟s7， 係選擇對應該厚度比值之第一薄膜與第二薄獏用以取代 該第一透鏡面與該第二透鏡面。 此外，上述實施例中所提及之該曲率半徑比值、該薄 膜變形量比值、該薄膜彈性係數比值的關係式其分別如下 所示。 ◎曲率半徑比值： "2 5與G係分別為該第 曲 min 其中，Ain係曲率半徑比值 率半徑與該第二曲率半徑。 ◎薄膜變形量比值： T = Alrl / Δ/γ2 其m系該薄膜變形量比值、…與A係分別為該 第一擴張變形量與該第二擴張變形量。 ◎薄臈彈性係數比值 τ=κ2/κ, 其中，Τ係該薄膜彈性係數比值、&與&係分別為該 弟一透鏡面之彈性係數與該第二透鏡面之彈性係數。 又’上述中該薄賴形量比值與該薄膜彈性係數比值 ''可用以蚊該第-薄難該第二薄_厚度比值 關係式係為： p T = Mrl /Alr2 = κ2 ΙΚΧ =： t2 ltx 其中’[與^係分別為該第—薄膜厚度與該第二薄膜厚 201222013 度再者，上述於步驟s 平均的方式，計算出 ，該等透鏡倍率係可藉由加權 施例中，兮 v均曲率半徑比值，例如，於一實 均係可根據該等透鏡倍率的高透鏡倍率 僧"。刀別地以正比地加權至對應的該曲率半徑201222013 VI. Description of the Invention: [Technical Jaw Domain of the Invention] The present invention relates to an aberration compensation method for a variable-focus liquid lens, and more particularly to an aberration compensation method for solving the aberration generated by a non-solid lens. [Prior Art] In the conventional optical system, the observation and enlargement of the object to be observed by the focusing and diverging characteristics of the lens by the lens is employed. However, the lens has a problem of aberration when observing the object to be observed, and the aberration problem affects the quality of the image at the same time, which may cause deformation or blurring. Among them, especially the part of the so-called spherical aberration, the problem of generating the spherical aberration is that the light is incident on the lens at different positions, so that the light is not focused on the same focus when it is focused by the lens. Upper, but only on a focal plane, thus creating a problem of aberrations. φ In order to solve the above problems, conventional techniques are used to eliminate the occurrence of aberrations by using an aspherical aberration lens or a composite lens, but these techniques are used on lenses made of transparent solids such as glass. It is not suitable for non-gj lenses, such as non-solid lenses such as liquid lenses. For example, a liquid lens is filled with a liquid in a lens such that the surface curvature of the film of the lens can be adjusted by the liquid to bring an outer or concave lens. Moreover, the change in the curvature of the surface is more suitable for the function of the liquid lens to have a variable focal length or a variable magnification, and the liquid lens is difficult or impossible due to the shape of the lens surface. It is adjusted to 201222013, so it is easy to produce serious spherical aberration problems at medium and high magnifications, which leads to poor image quality. Therefore, the present invention proposes a problem that can be solved to solve the problem of poor imaging of liquid lenses due to aberration problems. SUMMARY OF THE INVENTION The present invention provides an aberration compensation method for a variable focal length liquid lens, which is an average curvature of a minimum spherical aberration selected from all magnifications of a high magnification to a low magnification of the variable focus liquid lens. The radius ratio is further selected according to the thickness ratio of the corresponding film deformation amount ratio or the elastic modulus ratio of the first lens surface and the second lens surface to select an appropriate first film and second film to achieve all magnifications. The purpose of obtaining a small aberration is obtained. In order to achieve the above object, the present invention provides an aberration compensation method for a variable-focus liquid lens. Compensating for an aberration formed by the first lens surface and the second lens surface of the liquid lens, wherein the first lens surface has a first radius of curvature and the second lens surface has a second radius of curvature, the method comprising: In step si, the aperture of the variable focal length liquid lens, the thickness of the lens body and the refractive index of the liquid injected into the liquid lens are selected; in step S2, the aperture is selected, the thickness of the lens body and the refractive index are set. At least a multiple of the multiple lens magnification, and determining a combination of a plurality of curvature radii of the first lens surface and the second lens surface corresponding to one of the equal lens magnifications; in step S3, based on the selected ones a combination of curvature radii for calculating a complex spherical aberration corresponding to the combination of equal curvature radii; in step S4, selecting the smallest spherical aberration of the spherical aberrations to determine the minimum spherical aberration corresponding to 201222013 Combining the first and second lens faces required by the radius of curvature to generate a ratio of curvature radius; at step S5, the mirror surface is set to at least one of the lens magnifications Repeating the execution of the magic is performed in step S5 until all of the ratios of the curvature radii corresponding to the magnifications of the variable-focus liquid lens are obtained, and the variable is obtained according to the equal-angle ratio The average radius of curvature of the focal length liquid lens=value; in step S6, calculating and selecting a film deformation Lurie ratio or elastic coefficient corresponding to the first lens surface and the second lens surface according to the selected average radius of curvature ratio a thickness ratio of the ratio; and, in S7, selecting the first film and the second film corresponding to the thickness ratio to replace the first lens surface and the second lens surface. Compared with the prior art, the present invention It is used to solve the problem of the aberration generated by the conventional non-solid lens, which is difficult or impossible to adjust due to the shape of the non-solid lens surface, especially when the non-solid lens is at a high magnification. When used, it will cause serious spherical coma problems, which will inevitably affect the imaging quality of non-solid lenses. However, with the aberration compensation method proposed by the present invention, it is possible to surely achieve the objective of obtaining small aberrations at all magnifications. Furthermore, the present invention can verify that minor aberrations can be obtained at all magnifications by simulation and actual operation. [Embodiment] In order to fully understand the object, features and effects of the present invention, the present invention will be described in detail by the following specific embodiments and the accompanying drawings, and the description will be as follows: 201222013 2 and 2 are a schematic view and a flow chart of an aberration compensation method of the variable focal length liquid lens of the present invention. In FIG. 1 , the aberration compensation method of the variable focal length liquid lens is for compensating for the aberration S formed by the first lens surface 22 and the second lens surface 24 of the liquid lens 2 (ie, |FP-FM| The first lens surface 22 has a first radius of curvature q and the second lens surface 24 has a second radius of curvature r2. In FIG. 2, the aberration compensation method of the variable focal length liquid lens comprises: starting from step S1, selecting the aperture A of the variable focal length liquid lens 2, the thickness d of the lens body, and injecting the liquid in the liquid lens 4 The refractive index η. Next, in step S2, at least one of the multiple lens magnifications is set after selecting the aperture, the thickness of the lens body and the refractive index, and determining the first lens surface and the second corresponding to one of the equal lens magnifications. The combination of the complex curvature radii of the lens faces. Next, in step S3, based on the selected combinations of the curvature radii, the complex spherical aberration corresponding to the combination of equal curvature radii is calculated; and then, in step S4, the smallest spherical aberration among the spherical aberrations is selected. The first lens face and the second lens face required to combine the radius of curvature corresponding to the minimum of the spherical aberration are determined to produce a ratio of curvature radius. Next, in step S5, at least one of the lens magnifications is set to repeatedly perform the steps S2 to S5 until the curvature radius ratios corresponding to all the lens magnifications of the variable-focus liquid lens are respectively obtained. And obtaining an average radius of curvature ratio of the variable focus liquid lens according to the ratio of the curvature radius. Step S6, calculating, according to the selected average radius of curvature ratio, a thickness ratio of the film deformation amount ratio or the film elastic coefficient ratio corresponding to the first lens surface and the second lens surface in 201222013; and, in step s7 The first film and the second thin film corresponding to the thickness ratio are selected to replace the first lens surface and the second lens surface. Further, the relationship between the ratio of the radius of curvature, the ratio of the deformation amount of the film, and the ratio of the modulus of elasticity of the film mentioned in the above embodiments are as follows. ◎ Curvature radius ratio: "2 5 and G are the first song min, respectively, Ain is the radius of curvature ratio radius and the second radius of curvature. ◎ Film deformation amount ratio: T = Alrl / Δ / γ2 The m-based film deformation amount ratio, ... and the A system are the first expansion deformation amount and the second expansion deformation amount, respectively. ◎ Thin elastic modulus ratio τ = κ2 / κ, wherein the ratio of the elastic coefficient of the tantalum film, && is the elastic coefficient of the lens surface of the younger brother and the elastic coefficient of the second lens surface. In addition, the ratio of the ratio of the thin shape to the elastic modulus of the film can be used to determine the relationship between the second thin and the thickness ratio of the mosquito: p T = Mrl /Alr2 = κ2 ΙΚΧ =: t2 Ltx where '[and ^ are respectively the first film thickness and the second film thickness 201222013 degrees, and the above-mentioned averaging in step s, it is calculated that the lens magnifications can be weighted by the application, 兮v mean radius of curvature ratio, for example, a solid lens magnification according to the lens magnification 僧". The tool is proportionally weighted to the corresponding radius of curvature
亦即越高透鏡倍率獲得較高的加權值；反之則獲得 較低的加權值。 J 右將液體注人由上述本發明之方法所選定之該第一薄 I該第二薄膜所組成之該液體透鏡中，其該液體因而使 得該第—薄駭該第二薄臈由内向外凸擴張而產生之擴張 變形量，其中該擴張變形量與該第一薄膜或該第二薄膜所 刀別對應的該第-曲率半徑或第二曲率半徑的關係式係可 表示為： △/ί=2.(ΠΰΓν»4) 其中，Δ/|係該擴張變形量、η係該第一曲率半徑或該 第二曲率半#、〜係該口徑以H為1或2。 故藉由上述步驟’係可利用已選擇的該第一薄膜與第 一薄膜的參數製作該可變焦距液體透鏡，並可在所有倍率 下（包含低倍率、中倍率或高倍率）獲得較小的像差，亦即本 發明可於所有倍率之下皆能獲得很好的成像品質。此外， 若將該第一薄膜與該第二薄膜中其薄膜厚度較大者朝向一 待觀察物進行觀測，則可更加地產生更小的像差。 參考第3圖’係說明利用上述實施例所應用之模擬示 意圖。於第3圖中，係模擬可變焦距液體透鏡設定透鏡倍 率係為9的狀態下，其所對應到不同之第一曲率半徑^與 201222013 所對應之第二曲率半徑r2的所分別對應形成所有曲率半徑 組合的關係圖。 於模擬示意圖中，係表示當選定該第一曲率半徑Γι為 15.5mm且該第二曲率半徑Γ2為29.9mm時，可獲得最小像 差5 = 5.5mm。換言之，該曲率半徑的組合係可在透鏡倍率 係為9時獲得最佳曲率半徑比值；= /^ /厂2。 參考第4a與4b圖，係說明傳統技術與本發明係分別 地利用相同薄膜厚度與非相等薄膜厚度所造成像差補償之 籲比較示意圖。於第4a圖中，係傳統中利用薄膜厚度比值為 1之第一薄膜與第二薄膜所製作之可變焦距液體透鏡示意 圖，其成像效果僅於透鏡中間部分呈現最佳效果，其餘非 中心的周緣部分係產生嚴重的形變，其可同時—併參照其 對應的示意圖。 然而，比較第4b圖，其係利用本發明之方法所製作其 薄膜厚度比值為6之該第-薄膜與該第二薄膜之可變焦距 • 液體透鏡的示意圖，其成像效果不管是透鏡中間或周緣部 份’其皆可獲得較佳的成像效果，其可同時一併參考其對 應的示意圖。 與習知技術相較，本發明係用以解決習知利用非固體 式透鏡所產生像差的問題，其中該像差問題係由㈣_ 體式透鏡表面的形狀難以或無法進行調整的緣故。特別是 當該非固體式透鏡在高倍率使用時，更會產生嚴重之球面 像差問題’而該球面像差問題勢必會影響非固體式透鏡的 成像品質。然而’藉由本發明所提出之像差補償方法兄其 11 201222013 係可確實地達成可在所有倍率下可獲得較小像差之目的。 本發明在上文中已以較佳實施例揭露，然熟習本項技 術者應理解的是，該實施例僅用於描繪本發明，而不應解 讀為限制本發明之範圍。應注意的是，舉凡與該實施例等 效之變化與置換，均應設為涵蓋於本發明之範疇内。因此， 本發明之保護範圍當以下文之申請專利範圍所界定者為 準。 【圖式簡單說明】 第1圖係本發明之可變焦距液體透鏡之示意圖； 第2圖係本發明之可變焦距液體透鏡的像差補償方法之 流程圖； 第3圖係說明利用上述實施例所應用之模擬示意圖； 第4a圖係習知可變焦距液體透鏡的示意圖；以及 第4b圖係說明利用上述實施例所實際製作之已獲得像差 補償的可變焦距液體透鏡的示意圖。 【主要元件符號說明】 2 液體透鏡 22 第一透鏡面 24 第二透鏡面 4 液體 S 像差 Γι 第一曲率半徑 12 201222013 Γ2 第二曲率半徑 Α 口徑 d 鏡身厚度 η 折射率That is, the higher the lens magnification, the higher the weighting value; otherwise, the lower the weighting value. J is rightly injected into the liquid lens composed of the first thin film and the second film selected by the method of the present invention, wherein the liquid thus causes the first thin film to be from the inside to the outside The amount of expansion deformation caused by the convex expansion, wherein the relationship between the amount of expansion deformation and the first radius of curvature or the second radius of curvature corresponding to the first film or the second film can be expressed as: Δ/ί =2. (ΠΰΓν»4) where Δ/| is the amount of expansion deformation, η is the first radius of curvature or the second curvature half #, and the diameter is H or 1 or 2. Therefore, the variable length liquid lens can be made by using the parameters of the selected first film and the first film by the above steps, and can be obtained at all magnifications (including low magnification, medium magnification or high magnification). The aberration, that is, the invention can achieve good imaging quality under all magnifications. Further, if the first film and the second film have a larger film thickness toward the object to be observed, a smaller aberration can be generated more. Referring to Fig. 3, there is illustrated a schematic diagram applied by the above embodiment. In Fig. 3, in the state where the analog variable focal length liquid lens is set to a lens magnification ratio of 9, the corresponding first curvature radius ^ corresponds to the second curvature radius r2 corresponding to 201222013, and all of them are formed. A diagram of the combination of curvature radius. In the simulation diagram, it is indicated that when the first radius of curvature Γι is 15.5 mm and the second radius of curvature Γ2 is 29.9 mm, the minimum aberration 5 = 5.5 mm can be obtained. In other words, the combination of the radii of curvature can obtain the optimum radius of curvature ratio when the lens magnification is 9; = /^ / factory 2. Referring to Figures 4a and 4b, there is shown a schematic diagram of the comparison of the aberrations caused by the same film thickness and the unequal film thickness, respectively, between the conventional technique and the present invention. In Fig. 4a, a schematic diagram of a variable-focus liquid lens made by using a first film and a second film having a film thickness ratio of 1 is conventionally used, and the imaging effect is only effective in the middle portion of the lens, and the rest are non-central. The peripheral portion is severely deformed, which can be simultaneously - and reference to its corresponding schematic. However, comparing FIG. 4b, which is a schematic diagram of a liquid lens having a film thickness ratio of 6 for the first film and the second film by the method of the present invention, the imaging effect is either in the middle of the lens or The peripheral portion 'all of them can obtain a better imaging effect, which can be referred to the corresponding schematic diagram at the same time. In contrast to the prior art, the present invention is directed to solving the problem of the aberrations caused by the conventional use of a non-solid lens which is difficult or impossible to adjust by the shape of the (4)-type lens surface. In particular, when the non-solid lens is used at a high magnification, a serious spherical aberration problem is generated, and the spherical aberration problem necessarily affects the image quality of the non-solid lens. However, the aberration compensation method proposed by the present invention, 11 201222013, can surely achieve the goal of obtaining smaller aberrations at all magnifications. The invention has been described above in terms of the preferred embodiments thereof, and it is understood by those skilled in the art that the present invention is not intended to limit the scope of the invention. It should be noted that variations and permutations that are equivalent to the embodiments are intended to be within the scope of the present invention. Therefore, the scope of the invention is defined by the scope of the following claims. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic view of a variable focal length liquid lens of the present invention; FIG. 2 is a flow chart of a method for compensating for aberration of a variable focal length liquid lens of the present invention; FIG. 3 is a view illustrating the use of the above implementation A schematic diagram of a simulation applied to the example; a schematic view of a conventional variable-focus liquid lens in Fig. 4a; and a schematic view of a variable-focus liquid lens in which the aberration compensation has been actually obtained by the above embodiment is explained. [Main component symbol description] 2 Liquid lens 22 First lens surface 24 Second lens surface 4 Liquid S aberration Γι First radius of curvature 12 201222013 Γ2 Second radius of curvature Α Diameter d Body thickness η Refractive index
Pmin曲率半徑比值 T 薄膜彈性係數比值、薄膜變形量比值、厚度比值 Δ/Γ1 第一擴張變形量 Δ/,2 第二擴張變形量 Κι 第一透鏡面彈性係數 Κ2 第二透鏡面彈性係數 h 第一薄膜厚度 h 第二薄膜厚度 L 口徑 13Pmin curvature radius ratio T film elastic modulus ratio, film deformation ratio, thickness ratio Δ/Γ1 first expansion deformation amount Δ/, 2 second expansion deformation amount 第一 first lens surface elastic modulus Κ 2 second lens surface elastic coefficient h a film thickness h second film thickness L caliber 13