201040583 六、發明說明： ' 【發明所屬之技術領域】 ； 本發明涉及投影技術，特別涉及一種投影鏡頭。 【先前技術】 近年來，隨著投影技術之發展，消費者對投影晝面品 質之要求越來越高。因此，數位光處理投影儀及液晶顯示 投影儀所採用之數位微鏡元件（Digital micro-mirror device， ❹DMD)和液晶顯不面板（LCD panel)之圖兀在不斷提南。相應 地，具有低像差之投影鏡頭之市場需求也隨之增加。 【發明内容】 有鑒於此，有必要提供一種像差較小之投影鏡頭。 一種投影鏡頭，其從放大側至縮小側依次包括具有負 光焦度之第一鏡群和具有正光焦度之第二鏡群。所述第二 鏡群從放大側至縮小侧依次包括一具有正光焦度之前鏡群 ® 和一具有正光焦度之後鏡群。該投影鏡頭滿足條件式： -1.35<Fl/F<-0.35， 3<F24/F<5， 其中，F1為所述第一鏡群之焦距，F24為所述後鏡群之焦 距，F為投影鏡頭之總焦距。 本發明之投影鏡頭滿足條件式-1.35<Fl/F<-0.35和 3<F24/F<5，因此具有較小之畸變、慧差及像散等像差，使 其具有較好之成像品質。 5 201040583 ' 【實施方式】 : 下面將結合附圖，舉以下較佳實施方式並配合圖式詳 細描述如下。 圖1所示為本發明實施方式提供之投影鏡頭100,其用 於將一投影元件200如數位微鏡元件產生之影像投影到一 投影螢幕（圖未示）上。該投影鏡頭1〇〇從放大侧至縮小 側依次包括一具有負光焦度之第一鏡群10和一具有正光焦 ®度之第二鏡群20。所述放大側是指靠近投影螢幕之一側， 所述縮小側是指靠近投影組件200之一側。投影時，光線 自縮小側射入所述投影鏡頭100，依次經所述第二鏡群20 和第一鏡群10後，將圖像投影於所述投影螢幕上。 所述第一鏡群10從放大側至縮小側依次包括一第一透 鏡101、一第二透鏡102、一第三透鏡103、一第四透鏡104 及一第五透鏡105。 p 所述第二鏡群20從放大側至縮小側依次包括一具有正 光焦度之前鏡群22和一具有正光焦度之後鏡群24。該前鏡 群22從放大側至縮小側依次包括一第六透鏡221和一第七 透鏡222。所述後鏡群24從放大側至縮小側依次包括一第 八透鏡241、一第九透鏡242、一第十透鏡243、一第十一 透鏡244、一第十二透鏡245及一第十三透鏡246。其中， 所述第八透鏡241、第九透鏡242及第十透鏡243依次膠 合，形成一複合透鏡（圖未標），所述第十一透鏡244與第 十二透鏡245相互膠合。 6 201040583 為使該投影鏡頭100具有較好之廣角特性，該投影鏡 '頭100應滿足以下條件： ; (1) -1.35<Fl/F<-0.35， (2) 3<F24/F<5， 其中，F1為第一鏡群10之焦距，F24為第二鏡群20之後 鏡群24之焦距，F為該投影鏡頭100之總焦距。 條件（1)和（2)確保了第一鏡群10和第二鏡群20之後鏡 群24之焦距在整個投影鏡頭100中之比例，以使第一鏡群 〇 10產生之像差能得到較好之修正。條件（1)和（2)還可確保該 投影鏡頭100具有足夠之後焦長度，以便在所述第十三透 鏡246與投影元件200間設置其它光學元件。 優選地，該投影鏡頭100還滿足以下條件： (3) BF/F>4.5， 其中，BF為該投影鏡頭100之後焦距，即第十三透鏡246 之縮小側表面到投影元件200之距離。條件（3)用於確保該 q 投影鏡頭100之後焦距在一適當範圍内。 優選地，該投影鏡頭100還滿足以下條件： (4) -0.15<F/Ft<0.1， 其中，Ft為所述複合透鏡之焦距。條件（4)用於確保該複合 透鏡之光焦度在一適當範圍内，以使其產生之像差較小。 優選地，該投影鏡頭100還滿足以下條件： (5) n9>1.78 其中，n9為所述第九透鏡242在d光（波長為589.3nm) 條件下之折射率。條件（5)用於確保第九透鏡242具有高折 7 201040583 射率。當η9<1.78時，不利於該投影鏡頭100之高階色像差 •之修正。 - 所述投影鏡頭100還包括一孔徑光闌30及一玻璃片 40。所述孔徑光闌30位於所述第七透鏡222與第八透鏡241 之間，用於遮罩雜散光。所述玻璃片40設於所述第十三透 鏡246與投影元件200之間，用於防止所述投影元件200 受到灰塵之污染。 _ 所述第一透鏡101為非球面透鏡，其表面均滿足非球 〇 面之面型運算式： JC--. ch2 - ： + l + ^J\-(k + l)c2h2 其中，X是沿光軸方向在高度為h之位置以表面頂點作參考 距光軸之位移值，c為鏡面表面中心之曲率半徑，k是二次 曲面係數，h為從光軸到透鏡表面之高度，表示對Aihi 累加，i為自然數，Ai為第i階之非球面面型係數。 在本實施方式中，該投影鏡頭100之各光學元件滿足 ❹表 1 及表 2 之條件，且 2ω=109·8°，FNO.=2.35，F=7.42mm， FI = -6.35mm， F24=29.45mm，Ft=-86.71mm，BF=31.75mm。 表1中分別列有由放大侧至縮小側之各光學表面之曲 率半徑（R )、與後一光學表面之間距（D )、折射率（nd ) 和阿貝數（Abbe Number) ( Vd )。其中，請參閱圖1，S1至 S25依次表示從放大側至縮小側之各光學表面。 表1 R(nm) D(mm) nd Vd S1 249.568 5 1.525 55.951 S2 52.506 4.91 8 201040583 S3 60.66 4 1.620 36.259 S4 31.395 13.14 S5 58.75 3.5 1.589 61.253 S6 23.883 19.08 S7 68.864 3 1.589 61.253 S8 18.876 9.81 S9 -28.726 2.2 1.497 81.608 S10 55.919 2.33 S11 -1471.65 5.32 1.762 26.609 S12 -43.622 1.23 S13 33.492 9.11 1.569 56.044 S14 -64.372 22.67 孔徑光闌 00 0.42 S15 40.486 3.55 1.569 56.044 S16 -14.063 1.2 1.883 40.805 S17 15.197 9 1.569 56.044 S18 -39.378 0.36 S19 124.773 1.2 1.804 46.503 S20 24.776 3.15 1.497 81.608 S21 -47.457 0.1 S22 51.78 3.68 1.497 81.608 S23 -20.293 29.8275 S24 00 1.05 1.507 63.380 S25 00 1.1 各非球面表面之非球面係數如表2所示： 表2 k A4 A6 A8 A10 A12 A14 A16 S1 0 6.01E-6 -3.09E-9 9.66E-13 3.41E-17 -4.61E-20 -2.72E-23 1.11E-26 S2 0 3.80E-6 -2.49E-9 2.60E-14 -3.53E-16 3.39E-19 -4.05E-23 1.12E-26 本實施方式中所述投影鏡頭100之球差特性曲線、場 曲特性曲線及畸變之特性曲線分別如圖2、圖3及圖4所 示。圖2中，曲線f，d及c分別為該投影鏡頭100在f光（波 9 201040583 長為486.1nm)、d光（波長為589.3nm)及c光（波長為656.3nm) -條件下之球差特性曲線。可見，該投影鏡頭100產生之球 :差被控制在約-0.04mm〜0.18mm之間。圖3中，曲線t及s 分別為該投影鏡頭100在d光條件下之子午場曲（tangential field curvature)特性曲線及弧矢場曲（sagittal field curvature )特性曲線。可見，子午場曲值及弧矢場曲值被控 制在約-0.06mm〜0.16mm之間。圖4所示為該投影鏡頭100 _在d光條件下之畸變特性曲線。可見，畸變量被控制在約 〇 -1.6%〜0之間。綜前，投影鏡頭100產生之球差、場曲及畸 變被控制（修正）在較小之範圍内。 本發明之投影鏡頭滿足條件式-1.35<Fl/F<-0.35和 3<F24/F<5，因此具有較小之畸變、慧差及像散等像差，使 其具有較好之成像品質。 綜上所述，本發明符合發明專利要件，爰依法提出專 利申請。惟，以上所述者僅為本發明之較佳實施方式，本 〇發明之範圍並不以上述實施方式為限，舉凡熟悉本案技藝 之人士援依本發明之精神所作之等效修飾或變化，皆應涵 蓋於以下申請專利範圍内。 【圖式簡單說明】 圖1為本發明實施方式提供之投影鏡頭之示意圖。 圖2為圖1中之投影鏡頭之球差特性曲線圖。 圖3為圖1中之投影鏡頭之場曲特性曲線圖。 圖4為圖1中之投影鏡頭之畸變特性曲線圖。 201040583 Ο ❾ 【主要元件符號說明】 投影鏡頭 1〇〇第一鏡群 10 第一透鏡 101第二透鏡 102 第三透鏡 103第四透鏡 104 第五透鏡 105第二鏡群 20 前鏡群 22第六透鏡 221 第七透鏡 222後鏡群 24 第八透鏡 241第九透鏡 242 第十透鏡 243第十一透鏡 244 第十二透鏡 245第十三透鏡 246 孔徑光闌 30玻璃片 40 投影元件 200第一透鏡放大侧表面 S1 第一透鏡縮小侧表面 S2第二透鏡放大侧表面 S3 第二透鏡縮小侧表面 S4第三透鏡放大側表面 S5 第三透鏡縮小侧表面 S6第四透鏡放大側表面 S7 第四透鏡縮小侧表面 S8第五透鏡放大侧表面 S9 第五透鏡縮小侧表面 S10第六透鏡放大侧表面 S11 第六透鏡縮小侧表面 S12第七透鏡放大侧表面 S13 第七透鏡縮小側表面 S14第八透鏡放大側表面 S15 第八透鏡縮小侧表面 第九透鏡放大側表面 弟九透鏡縮小侧表面 S16 第十透鏡放大侧表面 S17 第十透鏡縮小側表面 S18第十一透鏡放大側表面 S19 第十一透鏡縮小側表面 S20第十二透鏡縮小側表面 S21 11 201040583 第十二透鏡放大側表面 - 第十三透鏡放大側表面 S22第十三透鏡縮小側表面 : 玻璃片放大側表面 S24玻璃片縮小側表面 S23 S25201040583 VI. Description of the invention: 'The technical field to which the invention pertains>> The present invention relates to projection technology, and more particularly to a projection lens. [Prior Art] In recent years, with the development of projection technology, consumers have become more and more demanding on the quality of projections. Therefore, the digital micro-mirror device (DMD) and the liquid crystal display panel (LCD panel) used in digital light processing projectors and liquid crystal display projectors are constantly being introduced. Accordingly, the market demand for projection lenses with low aberrations has also increased. SUMMARY OF THE INVENTION In view of the above, it is necessary to provide a projection lens having a small aberration. A projection lens comprising, in order from the magnification side to the reduction side, a first mirror group having a negative power and a second mirror group having a positive power. The second mirror group includes, in order from the magnification side to the reduction side, a mirror group having positive refractive power and a mirror group having positive refractive power. The projection lens satisfies the conditional expression: -1.35<Fl/F<-0.35, 3<F24/F<5, where F1 is the focal length of the first mirror group, and F24 is the focal length of the rear mirror group, F Is the total focal length of the projection lens. The projection lens of the present invention satisfies the conditional expressions -1.35 <Fl/F<-0.35 and 3<F24/F<5, and thus has aberrations such as distortion, coma and astigmatism, so that it has better imaging. quality. 5 201040583 'Embodiment: The following preferred embodiments will be described in detail below with reference to the accompanying drawings. FIG. 1 shows a projection lens 100 according to an embodiment of the present invention for projecting an image generated by a projection element 200, such as a digital micromirror device, onto a projection screen (not shown). The projection lens 1A includes, in order from the magnification side to the reduction side, a first lens group 10 having a negative power and a second lens group 20 having a positive power. The magnification side refers to a side close to the projection screen, and the reduction side refers to a side close to the projection assembly 200. At the time of projection, the light is incident on the projection lens 100 from the reduced side, and sequentially passes through the second mirror group 20 and the first mirror group 10, and the image is projected on the projection screen. The first lens group 10 includes a first lens 101, a second lens 102, a third lens 103, a fourth lens 104 and a fifth lens 105 in order from the magnification side to the reduction side. The second mirror group 20 includes, in order from the magnification side to the reduction side, a mirror group 22 having positive refractive power and a mirror group 24 having positive refractive power. The front lens group 22 includes a sixth lens 221 and a seventh lens 222 in order from the magnification side to the reduction side. The rear mirror group 24 includes an eighth lens 241, a ninth lens 242, a tenth lens 243, an eleventh lens 244, a twelfth lens 245, and a thirteenth in order from the magnification side to the reduction side. Lens 246. The eighth lens 241, the ninth lens 242, and the tenth lens 243 are sequentially glued to form a composite lens (not shown), and the eleventh lens 244 and the twelfth lens 245 are glued to each other. 6 201040583 In order to make the projection lens 100 have better wide-angle characteristics, the projection lens 'head 100 should satisfy the following conditions:; (1) -1.35 <Fl/F<-0.35, (2) 3<F24/F< 5, wherein F1 is the focal length of the first mirror group 10, F24 is the focal length of the mirror group 24 after the second mirror group 20, and F is the total focal length of the projection lens 100. The conditions (1) and (2) ensure the ratio of the focal length of the mirror group 24 after the first mirror group 10 and the second mirror group 20 in the entire projection lens 100, so that the aberration generated by the first mirror group 10 can be obtained. Better correction. Conditions (1) and (2) also ensure that the projection lens 100 has a sufficient back focus length to provide other optical elements between the thirteenth lens 246 and the projection element 200. Preferably, the projection lens 100 further satisfies the following conditions: (3) BF/F> 4.5, where BF is the focal length of the projection lens 100, that is, the distance from the reduced side surface of the thirteenth lens 246 to the projection element 200. Condition (3) is for ensuring that the focal length of the q projection lens 100 is within an appropriate range. Preferably, the projection lens 100 further satisfies the following condition: (4) -0.15 < F/Ft < 0.1, wherein Ft is the focal length of the composite lens. Condition (4) is for ensuring that the power of the composite lens is within an appropriate range so that the aberration generated therefrom is small. Preferably, the projection lens 100 further satisfies the following conditions: (5) n9 > 1.78 wherein n9 is the refractive index of the ninth lens 242 under the condition of d light (wavelength of 589.3 nm). Condition (5) is for ensuring that the ninth lens 242 has a high fold 7 201040583 luminosity. When η9 < 1.78, it is not conducive to the correction of the high-order chromatic aberration of the projection lens 100. The projection lens 100 further includes an aperture stop 30 and a glass sheet 40. The aperture stop 30 is located between the seventh lens 222 and the eighth lens 241 for masking stray light. The glass sheet 40 is disposed between the thirteenth lens 246 and the projection element 200 for preventing the projection element 200 from being contaminated by dust. The first lens 101 is an aspherical lens, and the surface thereof satisfies the surface type of the aspherical surface: JC--. ch2 - : + l + ^J\-(k + l)c2h2 where X is In the direction of the optical axis at the height h, the surface vertex is used as the reference displacement value from the optical axis, c is the radius of curvature of the center of the mirror surface, k is the quadric surface coefficient, and h is the height from the optical axis to the lens surface. For Aihi accumulation, i is a natural number, and Ai is the aspherical surface coefficient of the i-th order. In the present embodiment, the optical components of the projection lens 100 satisfy the conditions of Tables 1 and 2, and 2ω=109·8°, FNO.=2.35, F=7.42 mm, FI=−6.35 mm, F24= 29.45 mm, Ft = -86.71 mm, BF = 31.75 mm. Table 1 lists the radius of curvature (R) of each optical surface from the enlarged side to the reduced side, the distance from the latter optical surface (D), the refractive index (nd), and the Abbe Number (Vd). . Here, referring to Fig. 1, S1 to S25 sequentially indicate the respective optical surfaces from the magnification side to the reduction side. Table 1 R(nm) D(mm) nd Vd S1 249.568 5 1.525 55.951 S2 52.506 4.91 8 201040583 S3 60.66 4 1.620 36.259 S4 31.395 13.14 S5 58.75 3.5 1.589 61.253 S6 23.883 19.08 S7 68.864 3 1.589 61.253 S8 18.876 9.81 S9 -28.726 2.2 1.497 81.608 S10 55.919 2.33 S11 -1471.65 5.32 1.762 26.609 S12 -43.622 1.23 S13 33.492 9.11 1.569 56.044 S14 -64.372 22.67 Aperture stop 00 0.42 S15 40.486 3.55 1.569 56.044 S16 -14.063 1.2 1.883 40.805 S17 15.197 9 1.569 56.044 S18 -39.378 0.36 S19 124.773 1.2 1.804 46.503 S20 24.776 3.15 1.497 81.608 S21 -47.457 0.1 S22 51.78 3.68 1.497 81.608 S23 -20.293 29.8275 S24 00 1.05 1.507 63.380 S25 00 1.1 The aspheric coefficients of the aspherical surfaces are shown in Table 2: Table 2 k A4 A6 A8 A10 A12 A14 A16 S1 0 6.01E-6 -3.09E-9 9.66E-13 3.41E-17 -4.61E-20 -2.72E-23 1.11E-26 S2 0 3.80E-6 -2.49E-9 2.60E -14 -3.53E-16 3.39E-19 -4.05E-23 1.12E-26 The spherical aberration characteristic curve, field curvature characteristic curve and distortion characteristic curve of the projection lens 100 in the present embodiment are respectively 2, 3 and 4 shown in FIG. In FIG. 2, curves f, d, and c are respectively the projection lens 100 under the conditions of f light (wave 9 201040583 length 486.1 nm), d light (wavelength 589.3 nm), and c light (wavelength 656.3 nm). Spherical difference characteristic curve. It can be seen that the ball produced by the projection lens 100 has a difference of between about -0.04 mm and 0.18 mm. In FIG. 3, the curves t and s are the tangential field curvature characteristic and the sagittal field curvature characteristic of the projection lens 100 under the condition of d light, respectively. It can be seen that the meridional curvature value and the sagittal curvature value are controlled to be between about -0.06 mm and 0.16 mm. Figure 4 shows the distortion characteristic of the projection lens 100_ under d-light conditions. It can be seen that the distortion variable is controlled between about -1.6%~0. In general, the spherical aberration, field curvature and distortion produced by the projection lens 100 are controlled (corrected) to a small extent. The projection lens of the present invention satisfies the conditional expressions -1.35 <Fl/F<-0.35 and 3<F24/F<5, and thus has aberrations such as distortion, coma and astigmatism, so that it has better imaging. quality. In summary, the present invention complies with the requirements of the invention patent and submits a patent application according to law. However, the above-mentioned embodiments are merely preferred embodiments of the present invention, and the scope of the present invention is not limited to the above-described embodiments, and those skilled in the art will be able to make equivalent modifications or variations in accordance with the spirit of the present invention. All should be covered by the following patent application. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic view of a projection lens according to an embodiment of the present invention. FIG. 2 is a graph showing spherical aberration characteristics of the projection lens of FIG. 1. FIG. FIG. 3 is a graph showing the field curvature characteristics of the projection lens of FIG. 1. FIG. 4 is a graph showing distortion characteristics of the projection lens of FIG. 1. 201040583 Ο ❾ [Description of main component symbols] Projection lens 1 〇〇 first mirror group 10 first lens 101 second lens 102 third lens 103 fourth lens 104 fifth lens 105 second mirror group 20 front mirror group 22 sixth Lens 221 seventh lens 222 rear mirror group 24 eighth lens 241 ninth lens 242 tenth lens 243 eleventh lens 244 twelfth lens 245 thirteenth lens 246 aperture stop 30 glass piece 40 projection element 200 first lens Amplifying side surface S1 First lens reducing side surface S2 Second lens amplifying side surface S3 Second lens reducing side surface S4 Third lens amplifying side surface S5 Third lens reducing side surface S6 Fourth lens amplifying side surface S7 Fourth lens shrinking Side surface S8 Fifth lens magnification side surface S9 Fifth lens reduction side surface S10 Sixth lens magnification side surface S11 Sixth lens reduction side surface S12 Seventh lens magnification side surface S13 Seventh lens reduction side surface S14 Eighth lens magnification side Surface S15 Eighth lens reduction side surface Ninth lens magnification side surface Young nine lens reduction side surface S16 Tenth lens magnification side surface S17 Ten lens reduction side surface S18 eleventh lens magnification side surface S19 eleventh lens reduction side surface S20 twelfth lens reduction side surface S21 11 201040583 twelfth lens magnification side surface - thirteenth lens magnification side surface S22 tenth Three lens reduction side surface: Glass sheet magnification side surface S24 Glass sheet reduction side surface S23 S25
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