gr 曲率大小的单位是“屈光度”(Dioptre),等于每米的弧度 riemann 只要空間每一可測量區域的有效曲率不是顯著地與零不同,則在每一點。曲率在三個方向上的測量都可具有任意值
"假如量度速度向量時不用歐氏度量,而是用隨點變動的內積
< >x,我們還是可以定義動能
。
在空間每一點都可以變動的內積,即是說給出了黎曼度量,可以寫作一個張量 。"
[PPT]近代幾何的發展 丘成桐香港中文大學數學科學研究所
www.cms.zju.edu.cn/UploadFiles/AttachFiles/20054411421524.ppt
假如量度速度向量時不用歐氏度量,而是用隨點變動的內積< >x,我們還是可以定義 動能 。 在空間每一點都可以變動的內積,即是說給出了黎曼度量,可以寫作一個張 ...
www.cms.zju.edu.cn/UploadFiles/AttachFiles/20054411421524.ppt
假如量度速度向量時不用歐氏度量,而是用隨點變動的內積< >x,我們還是可以定義曲率波_百度百科
baike.baidu.com/view/2669166.htm
轉為繁體網頁
... 着转动时,转动产生的坑产生曲率波,以光速向外传播。波动在黑洞周围的时空体形成漩涡的波纹,每一点曲率波都会向外辐射开去就像高速旋转的浇水器喷出的水。轉為繁體網頁
用"曲率波"造句- "查查"在線詞典 - 綫上翻譯
tw.ichacha.net/zaoju/曲率波.html
波動在黑洞周圍的時空體形成漩渦的波紋,每一點曲率波都會向外輻射開去就像高速旋轉的澆水器噴出的水。 5. 當視界旋轉時,啞鈴型黑洞輻射出去曲率波反作用在 ...- A new reality
- The dealer folds
- Investors play their hand
Mile wide, inch deep
Bond market liquidity dries up
Mile wide, inch deep
Bond market liquidity dries up
A new reality
Dan Fuss likes to describe the structure of the corporate bond market as resembling an ice cream sandwich: bonds change hands between the two crispy wafers on either side, but there’s a fluffy layer in between that facilitates each transaction.
“It’s a good sandwich if there’s a whole bunch of ice cream on the inside,” says Fuss, a bond market veteran who runs the $21.9 billion Loomis Sayles Bond Fund. But in recent years, that creamy inner layer, commonly known by the less appetizing title of “dealer,” has been melting.
Dealers were once powerful arms of Wall Street’s biggest investment banks, such as Merrill Lynch, J.P. Morgan and Lehman Bros. They used their large trading desks to make markets for investors to buy and sell securities. But the shifting roles of these large banks since the financial crisis, often pinned on financial regulations like the Volcker Rule, has caused a steep drop in the volume of debt securities these investment banks hold.
The cushion protecting fixed-income investors from market shocks, particularly in the $6.6 trillion corporate bond market, is melting, which is creating a new form of risk when it comes to buying these securities. In response, investors are reevaluating how they hold bonds sold by companies from Apple Inc. to Ford Motor Co. to DreamWorks Animation, as well as reshaping how they interact in the secondary trading market. The changes have served as a key factor eroding the traditional conviction that the bond market shields investors from risk.
Liquidity drought
Created by Terrence Horan
The financial crisis forced the surviving Wall Street banks to reduce risk in a hurry. Many have downgraded their roles as market-makers for corporate bonds, taking fewer bonds onto their books for future sale. Market participants blame the constricting regulatory forces of capital requirements and the post-crisis Volcker Rule. Regulators have pinned the blame back on the banks, which raced to shed less-liquid assets even before regulations were enacted.
At the same time, a surge in new bond sales has increased the size of the market even as dealers, the key facilitator to helping those bonds change hands in the secondary market, have become less willing to handle them. The result is a bond market which is flush with new securities but hobbled when it comes to pricing and trading these securities after the initial sale. As liquidity evaporated in the wake of the financial crisis, it has adjusted the way large asset managers hold and trade bonds, which then impacts the retail investors who put money into mutual and exchange-traded funds (read one institutional investor's story). Here's what's at stake:
- Buyers are paying a premium to own liquid bonds
- Investors who need to sell bonds in a hurry are finding less stable prices
- A chaotic exit from the bond market could cause yields to spike and portfolio values to drop
These market shifts are set against the backdrop of a widespread fear that investors will leave the bond markets en masse as interest rates rise. Concerns about low bond-market liquidity mounted this summer as investors ditched bonds in what bond guru Jeffrey Gundlach has called a liquidation cycle (see what investors were saying at the time). The 10-year Treasury note yield spiked by more than 1.3 percentage points over the summer, briefly touching 3%, on concerns about a Federal Reserve wind down of its bond-buying stimulus program, which was announced last week. The benchmark note traded near 3% on Dec. 27.
The summer bond selloff propelled the corporate bond market to a brief correction characterized by wild movements in prices, though investment-grade prices rapidly recovered. If an event in the credit or rates market provokes another panicked rush to the exits, without the help of dealers as a cushion, it could strain the market and further exacerbate price swings. The fear is that what might have been a moderate selloff could cascade into a rout, sending costs on mortgages and corporate debt sky high.
“I think people have gotten too comfortable, nay complacent, with how this exit process works,” says Tom Murphy, sector leader for investment grade credit at Columbia Management. Investors have piled money into corporate bonds in the years since the financial crisis, but that could translate to chaos if sentiment reverses all at once.
But there’s always a silver lining, and the liquidity struggles facing the market may finally be heralding a broader discussion about whether and how the bond market can better meet the needs of investors. Buyers of debt would ideally like to be able to trade large blocks of bonds quickly and cheaply. The holy grail for many investors is something akin to the way equities trade: in high volumes with tight differentials between the price of a buyer and seller.
Fragmentation
"The market is a mile wide and an inch deep.” — Will Rhode, director of fixed income, TABB Group.
That’s a difficult proposition, if not impossible. The corporate bond market is by nature fragmentary: while a company has one ticker symbol on a stock exchange, that same firm can have dozens of outstanding bonds, each with their own peculiarities. The wide range of differentiation allows companies easier capital markets access and it provides opportunities for investors who can parse the relative value of different issuances. It’s also at the heart of what makes it so hard to ensure a liquid market.
“The market is a mile wide and an inch deep,” says Will Rhode, director of fixed income at research firm TABB Group.
With liquidity making trading more difficult in the corporate bond market, there’s a growing recognition that a solution is needed, and that it may have to go beyond simply adjusting the point of interaction between dealers and investors. The whole market may need to evolve -- from standardizing the way bonds are issued to funneling the market toward a new trading structure.
The issue has long been top-of-mind among market insiders, but isn’t as widely discussed among the vast pool of investors who buy into the bond market for its perceived security. MarketWatch interviewed a range of corporate bond market participants in recent months to assess the origins of this shift, the reconsideration of trading strategies that it’s spurred among bond investors, and a possible path towards a better functioning bond market.
The dealer folds
Before the financial crisis, dealer market-making held a powerful place in the nation’s biggest investment banks. The fresh-out-of-college traders that shuffled in and out of Manhattan bank buildings each day handled the banks' inventories of bonds worth hundreds of millions of dollars, which they used as starting capital to make their own trades, says Lawrence McDonald, a former Lehman Bros. corporate bond trader. The holdings, which were used to make markets for each type of corporate security, would fit into two categories, or books.
“The front book is the facilitation book. That’s the book for client liquidity. The back book is your prop position. That book was responsible for a lot of profits on the Street in 2007, and that today pretty much doesn’t exist,” said McDonald, who authored A Colossal Failure of Common Sense, a bestseller about the bank's demise.
That system crumbled in the years after the financial crisis. The facilitation books shrank in size while the proprietary trading books became virtually non-existent. Dealer balance sheet sizes fell to a fraction of what they once were.
The smaller amount that dealers hold on their books means they can’t unconditionally buy bonds that investors are trying to sell, especially in large blocks. But there’s another issue at play: the low interest-rate environment that characterized much of the post-crisis economy has brought many new issuers into the market. New corporate bond sales have surged as issuers rushed to take advantage of still attractive rates and investors sought the relatively higher income of corporate debt.
The combination of smaller holdings by dealers and a surge in the amount of outstanding corporate debt suggests that there’s more inventory to change hands with fewer institutions willing to facilitate those transactions. Whereas dealers once held about 4% of all outstanding corporate debt on their balance sheets, they now hold closer to 0.5%, according to Oliver Randall, a professor of finance at Emory University, who has done research on corporate bond market liquidity (see more about his research).
Even as most sides recognize there’s a lack of liquidity in the market, there’s a fundamental disagreement about what caused it. Market participants are quick to point to new regulations that limit proprietary trading by dealers and increase the amount of reserves required to be held by banks. In that sense, the liquidity drought has provided ammunition for critics who believe financial reform has been destructive to the markets. But government officials are equally quick to suggest that banks have become less tolerant of risk.
The Volcker Rule was passed as part of the Dodd-Frank financial reform bill in 2010. It banned banks from trading securities with their own money, or proprietary trading. The rule has become one of the more controversial pieces of the regulatory regime, even though the final regulations were only laid out in early December. Nonetheless, banks had already wound down their proprietary trading operations in anticipation of the rule taking effect, and market participants say the lack of clarity about how much of dealers' standard trading activity would be considered proprietary further cut into their market-making ability ahead of the release of the final regulations (read NYSE CEO Niederhauer's take on the Volcker Rule and bond markets) .
The other focal point of regulatory reform is the Basel III capital regulations, which force banks to hold higher levels of reserves as a buffer against the type of bank leverage that expedited Lehman's fall into bankruptcy and kicked off the financial crisis. It’s making the dealer arms of banks less able to deploy capital to make markets in corporate bonds, market-makers told Treasury officials .
Lawmakers have cited broader shifts in trading practices as possible reasons for the decline in market-making ability.
New York Federal Reserve economists did research on the summer 2013 bond selloff, looking at how market-making ability changed as investors left the bond market as a whole. They concluded that even though dealers stepped back from their roles as intermediaries during the selloff, the dealers for whom there was more regulatory breathing room to take on risk actually took less risk. That indicated market-making ability was driven less by capacity limitations from regulations, and more by self-imposed limits on risk.
Finger pointing aside -- and excluding other reasons, such as hesitancy of trading outside the benchmarks set by pricing-disclosure platform Trace -- there tends to be a widespread recognition that the historic ability to take on risk has evaporated, forcing a shift in the way investors trade bonds. The bottom line, says Fuss of Loomis Sayles, is that it’s, “rules, both written and internal, as to the risk [dealers] can take carrying inventory.”
Investors play their hand
The total amount of trades in the high-grade corporate bond market has actually increased in the last five years, which seemingly contradicts the idea that liquidity is drying up. But alongside that rise, trade sizes have shrunk markedly, indicating that investors trying to route their trades through Wall Street have had to break up their trades to accommodate smaller balance sheets.
This change has given small firms an unusual advantage on Wall Street, where mammoth investors often have an edge because of their size.
Trade size
“I haven’t seen any problems with liquidity, but the size I trade in isn’t really a problem.” — Chris Keith, Adviser Investments
Chris Keith manages portfolios for individuals at Newton, Mass.-based Adviser Investments, which has roughly $2 billion in assets under management. When he’s in the market, he’s trading in smaller quantities than the major asset managers, which means he doesn’t risk overwhelming the Street with his inventory.
“I haven’t seen any problems with liquidity, but the size I trade in isn’t really a problem,” Keith said. “I think it’s when you have bigger trades, you get a concern there.”
For larger investors, another trick to circumvent liquidity issues is to deal in more liquid synthetic securities such as derivatives contracts, which can be used to bet on the credit quality of a company without having to deal with the same liquidity problems of the bond market.
Douglas Peebles, chief investment officer and head of AllianceBernstein fixed income, says he finds himself using more derivatives. These allow buyers to invest in the same underlying assets, but in many cases, they can be assured of more liquidity that the actual bond. Bond guru Bill Gross, who runs the world’s biggest bond fund, also concedes that he has begun using derivatives in his Pimco Total Return Fund.
Peebles has also shifted the way his trading desk works. His traders now have experience in independently pricing the debt securities they’re looking to buy and sell, reducing reliance on dealers to provide fair prices for trades.
“Before, you could go into the marketplace, and go ask five guys for the price of a bond, and get five similar prices. Now, we need to know the price,” he said.
Assessing the inherent value of a bond also includes knowing the price premium of liquidity. There's a growing gap between which bonds are liquid and which ones aren't, so the more liquid a bond is the higher the price tends to be, and the lower the yield.
A November Goldman Sachs report estimates that the premium that a bond pays over Treasurys is roughly 10% larger when a bond is illiquid, a large increase over pre-crisis levels. Shown the other way, liquid bonds on average yielded about 0.1 percentage points less between 2011 and mid-2013, according to BlackRock. That may not seem like much, but in a low-rate environment, every basis point counts over the life of a bond.
As investors adjust to this environment, innovation is beginning to take shape. Electronic-trading networks, which provide a more efficient connection between investors and dealers as well as other investors, have been slowly catching on (Read about MarketAxess as a case study). Such platforms run the gamut: some simply connect an investor to a dealer in a computerized equivalent of a phone call, while some open up the possibility of trading between all investors and all dealers at the same time.
Market participants have also been gravitating toward a variety of new market structures that redefine how corporate bonds trade (Rhode, of Tabb Group, puts these new structures into three groups).
The bottom line is that bond investors are getting used to the idea that liquidity has dried up. And here’s where the rubber meets the road. If all is calm in the bond market, with dependable and reliable flows into and out of bond funds, investors can methodically work around the issue. In that sense, a robust secondary market is simply a luxury.
But if there’s a mass exodus from the market, a functioning mechanism to trade bonds is necessary. Retail investors pulled money from corporate bond funds over the summer of 2013, forcing the sale of underlying assets, as the Federal Reserve contemplated scaling back its bond-buying program. When big bond investors had to sell into a down market, inconsistencies in the pricing became more exaggerated (See how investors fled bond funds this summer ).
The 10-year Treasury note, a benchmark often used to price sectors of the corporate bond market, recently traded near its highest level in over two years, though the corporate bond market recovered quickly from the summer selloff. If that sentiment again reverses -- a subject of much discussion due to shifts in monetary policy as well as any number of other market factors (see: the Great Rotation debate) -- a healthy trading mechanism is a necessity.
A solution may prove difficult because the bond market itself is fragmented, with issuers of many different sizes each selling specific types of debt. That was the case long before the financial crisis, but in the end the whole market may need to evolve, says Richard Prager, head of trading and liquidity strategies at BlackRock. The firm has been testing an internal bond trading platform (Read about BlackRock's Aladdin bond-trading platform). If trading in the bond market is to become like trading in the stock market, the adaptation has to begin with issuers, who could streamline the way they issue debt, with all of the other groups of market participants pitching in.
“This is a journey,” says Prager. “This is not an overnight market structure shift. I don’t know if this a three-year, five-year, or decade-long journey. In the equity market it took a decade to change.”
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屈光度编辑
本词条缺少名片图,补充相关内容使词条更完整,还能快速升级,赶紧来编辑吧!
屈光度是屈光力的大小单位,以D表示,既指平行光线经过该屈光物质,成焦点在1m时该屈光物质的屈光力为1屈光度或1D。以透镜而言,是指透镜焦度的单位如一透镜的焦距1m时,则此镜片的屈折力为1D屈光度与焦距或反应。
中文名
屈光度
属 性
物理学
大小单位
屈光力
单 位
D
目录
1简介编辑
光线由一种物体射入到另一种光密度不同的物质时,其光线的传播方向产生偏折,这种现象称为屈光现
象,表示这种屈光现象大小(屈光力)的单位是屈光度(缩写为“D”)。1D屈光力相当于可将平行光线聚焦在1米焦距上。
象,表示这种屈光现象大小(屈光力)的单位是屈光度(缩写为“D”)。1D屈光力相当于可将平行光线聚焦在1米焦距上。
眼睛折射光线的作用叫屈光,用光焦度来表示屈光的能力,叫做屈光度。眼睛不使用调节时的屈光状态,称为静态屈光,标准眼静态屈光的光焦度+58.64D。人眼在使用调节时的屈光状态,称为动态屈光,其光焦度强于静态屈光的光焦度。由于眼睛屈光度不正确,造成不能准确在视网膜成像,就是视力缺陷,一般情况需要佩带眼镜,通过镜片补充和矫正眼睛本身的屈光度,达到视网膜正确成像的目的!
屈光度,或称焦度,英语用“Dioptre”表示,是量度透镜屈光能力的单位。
焦距的倒数叫做透镜焦度,或屈光度,用φ表示。如果焦距是10cm,那么φ=10D。
凸透镜(如:远视镜片)的度数是正数(+),凹透镜(如:近视镜片)的度数是负数(-)。
一个+3屈光度的透镜,会把平行的光线聚焦在镜片的1/3米外。
屈光度的单位简写是D,国际单位制的单位是 m。
一般眼镜常使用度数来表示屈光度,以屈光度 D 的数值乘以 100 就是度数[1] ,例如 -1.0D 等于近视眼镜(凹透镜)的 100度。
2检查编辑
视网膜检影镜法
这是一种客观检查法。检查者手持视网膜镜(中央有孔的小圆反光镜),离开眼球1米远,将光线反射到眼球里。光线通过屈光间质到达视网膜,视网膜将光线原路反射出眼球。检查者通过视网膜镜中央的小圆孔,可以看到反射回来的光线。由于屈光间质的屈光能力不同,反射光的影像表现不同。影像与视网膜镜的移动方向一致,称为顺动,反之称为逆动。远视眼反射光的影像顺动,近视眼反射光的影像逆动。检查者为了使影像不动,需要不断在受检者的眼前加不同的眼镜片,加到影像静止为止,说明镜片已经中和了眼球的屈光不正。换句话说,镜片的屈光度就是眼球屈光不正的度数。
自动验光仪验光法
用自动检查仪代替检查者手里拿的视网膜镜和各种镜片。
3计算编辑
屈光力越强,焦距越短。2D屈光力的透镜焦距为1/2m或50cm。如果想知道透镜的焦距,用100cm,也就是1.00m除以屈光力,结果即为焦距。例如,5D屈光力的焦距为20cm。(100cm除以5D=20cm。)凸透镜的屈光力以“+”号表示,凹透镜的屈光力以“—”表示。 1 屈光度或 1D 等于常说的 100 度。
4调节编辑
在一些光学仪器上比如相机、望远镜、显微镜等器材上,都考虑到了使用者在不方便佩带眼镜观看时各人
眼睛的视力差异,所以都具有屈光度调节装置。因此,“屈光度”这个概念是眼镜的,如200度的近视镜屈光度为-2D,150度的老花镜的屈光度为+1.5D。KWP海岸线网络安全资讯站一些高档相机为了方便一些轻微近视或老花的人群不戴眼镜可以直接观看取景器内的效果增加了屈光度调节装置。屈光度调节装置其实就是在相机取景目镜处加一组镜片,通过旋钮等调整镜片位置关系,使其达到一定范围内的连续屈光度转换。范围一般在-3D到+2D之间。由于屈光度调节范围是有限的,超过这个范围的中度近视等用户可以另外选购专用的目镜调节镜。专为近视用户开发的目镜调节镜,屈光度分别为-1、-2、-3、-4等;专为远视用户开发的目镜调节镜,屈光度分别为+0.5、+1、+1.5、+2、+3等。用户可根据自己的视力情况,选择合适的目镜校正镜加装在目镜内,可以裸视进行拍摄。屈光度调节功能不仅在单反相机,并增加部分成本等原因,对于最重视小巧便携的卡片式数码相机一般都没有。屈光度可调眼镜根据现有通用矫正视力缺陷(近、远视眼)眼镜的镜片形状固定,屈光度不能调节的缺点,本实用新型将镜片分为镜片和透镜两部分;透镜又由锅底形里层、外层和液层三层构成。锅底形里层的周边,有一向外转折且与外层相连的透镜边,形成周边封闭的层状液体容纳空间。镜片外侧的镜片边上开有通液孔道,其一端开口于液层,一端与设置在镜片外侧的镜片边内的液压调节装置相连。当启动液压调节装置,使液层的液体压力渐渐加大时,则凹透镜的屈光度由大渐小,而凸透镜的屈光度则由小渐大;反之,凹透镜的屈光度由小渐大,而凸透镜的屈光度则由大渐小,由此实现眼镜屈光度的自由调节。?
5作用编辑
第一点
对于同种材料制成的凸透镜,其凸度越大,屈光度数越大,反之越小。换言之,对同一只眼球而言,近视度
第二点
眼球的屈光系统是个可调的“凸透镜”,因而形态可变,当眼前放上凹透镜时,眼球仍具有自我调节功能,眼睛能看清不同距离的目标和近视或老视患者戴镜能适应本身就说明了这一点。
第三点
由于普通眼镜与眼球相分离,形象直观,容易计算。本节探讨的重点是眼镜对眼球屈光的影响,对有关眼镜的论述,都是针对普通眼镜。戴角膜接触镜与普通眼镜在屈光方面具有相同的效果,其原理和技术在眼镜行业已经很成熟,因此不再论述。
第四点
在屈光学中,只有在某些特殊情况下,屈光度数为P1、P2两透镜组合产生的屈光效果才是屈光度为P1+P2的透镜。在眼球与透镜组成的光路中,在效果上或定性的计算中,也可以有P1+P2这种情况,这并非透镜组合后的实际屈光效果,而是一种简化和近似,因为眼睛具有自我改变屈光度的能力。虽然较难用实验验证,但从眼球的调节效果看,它应当具有抵消镜片屈光度的作用,而该公式却具有简化计算的作用。对于眼球和透镜所组成的系统来说,至多是两个透镜组成的屈光系统,因此可以利用屈光学理论进行计算。当戴上透镜时,因眼球特殊的调节作用,将透镜的屈光度和眼球调节适应后的屈光度相加减,也可得到近似值,虽然与准确地测量眼球的屈光力尚有一段距离,但在效果上却接近。在该论证中,尽管从理论上进行了推导,但实验和测量都非常困难,就象配制近视镜需要试戴一样,在用来指导配镜的过程中还要进行试验。
第五点
从眼球的屈光特点看,有人测得眼球的静屈光力为+58.6D,这虽然是一特例,但也基本反映出眼球具有很强
的屈光力,其调节相对较小,正常眼为0——10D左右,近视眼为n——10D(n指眼球的近视屈光度数)左右,而它又固定在眼眶内,因此对某一个人来说,可以认为眼球的屈光系统——“透镜”的中心到视网膜的距离不变,在以后的计算中,可认为像距为常数K,对于眼球的屈光来说,如果能在视网膜上成清晰的像,该屈光系统仍满足透镜成像公式
1/u+1/k=P
其中K是常数,P为眼球的屈光度数,是变量,意思是不同的人看不同距离的目标和不同的人眼球的屈光度数不同,U指目标到眼球的距离。该公式成立的条件是:某一时刻,眼睛看某一距离的目标,且目标在眼睛的近、远点之间。从公式看,正视眼看无穷远处时1/u=0,上式可化为P=1/K,可令1/k=P0,即P0为眼球的静屈光度。当看距眼球为L的目标时,“透镜”成像公式变为1/L+1/K=1/L+P0,1/L为眼球增加的屈光度数,1/L+P0即为眼球看距离为L的目标时的屈光度。
对于戴镜者来说,在一般情况下,眼球到眼镜中心的距离约为1.2——2.4CM,以下用h表示,但对于某人某一时刻的值是确定的,设屈光度为P'的透镜的焦距为F,当看距离为L的目标时,镜片成像公式如下:
1/L+1/V=P'==>1/V=P'-1/L①
此时透镜所成像到眼球这一“透镜”的距离为|V|+h,眼球的屈光情况满足公式:1/(|V|+h)+1/K=P②
从公式看,如果|V|比h大得多,根据①公式,②式可近似简化为:
1/|V|+1/K=D=|D'-1/L|+1/K③
由于眼睛透过透镜看到的是虚像,V<0,则1/|V|+1/K=1/L+1/K-D'=D1+D0-D'
从该公式看,|V|的大小取决于物距L和透镜的焦距,考虑到实际情况,近视眼镜的屈光度大多数大于-6D,学生看书、写字的距离大多大于0.25M,而且根据透镜成像公式可知,凹透镜屈光度数P'(注D'<0,下同)越小,V|越小,物距越小,|V|越小,如当D'=-5,U=0.25时,V|=0.111M,仍比0.02M大很多。所以作为理论
计算,在看距离不太近、镜片度数不太高的目标时,可忽略h,这样可简化计算,有利于定性分析。换言之,对于薄透镜来说,如果忽略眼球到镜片的距离,可以认为因戴近视眼镜致使眼球调节增加的调节度数等于透镜的屈光度数。在眼球与眼镜组成的光学系统中,各部分所产生的屈光度数可近似相加减,这种分析可使计算简化,使问题变得容易。在以后的论述中,我们将利用这一结果进行定性分析和近似计算。
第六点
误差分析。如果以公式为标准,那么产生误差的原因是多方面的,现对此分析。
(1)因为眼球的调节与形变同时进行,有调节就有形变,有形变就有眼球前后径的变化,还由于晶状体和角膜本身形变而导致的角膜、房水、晶状体所组成的“凸透镜”光心的变化。虽然近视或老视本身并不能说明其前后径的变化(一说,近视眼是眼球成像在视网膜前方,但近调节的过强或睫状肌不能放松都可实现这一点,不能充分说明眼球前后径变长),但更不能说明其不变性。这些因素的存在决定了公式中K只是一个近似,而且近调节幅度越大,K值变化越大,这是产生误差的一个原因。但考虑到在眼球调节中,晶状体的屈光度调节和眼球的屈光度(约60屈光度)相差很远,而眼球调节幅度一般少于10个屈光度,相对较小,角膜屈光度变化更小,因此,可认为“透镜”光心到视网膜的距离几乎不变。
(2)因每个人的眼球前后径不等,对不同的人而言,K并非常数,很难准确测量,但具体到某一个人的某一阶段而言,眼球前后径不变,可认为K是常数。
(3)对不同的人而言,眼镜片到“凸透镜”光学中心的距离是一较难测量的变量,这也影响到计算的准确性。由计算可知,h增大时,误差增大,反之越小。
第七点
在眼前放置透镜时,与正常眼相比,如果眼睛仍然能看清目标,从眼球的调节效果看,眼镜首先抵消眼球调节的不足,因此在以后的计算中,只要在眼球正常的调节范围内,用于抵消透镜的效果在理论上能够成立,我们无须注意眼球实际屈光度的变化。对眼球来说,不管戴多少屈光度的眼镜,要看清前面的目标,必须低消眼镜的作用而增加屈光度调节。
第八点
由于配镜误差、适应等原因,即使把各种因素都考虑进去,理论对于实践也只是一种近似,眼球调节幅度较大时,这种简单化、理想化的理论会因自身形变而使误差增大。再者,镜片到眼球光学中心的距离随不同的人而不同,这又无法用物理公式表示,在具体配制时要具体问题具体分析。
第九点
对于眼球和镜片所组成的屈光系统来说,镜片度数是确定的,而眼球的屈光度数却是个变量,因此,把眼球看成是一个可调凸透镜的意思是:眼睛透过眼镜能看清某一目标时,眼球的屈光度数确定,因而完全可以利用屈光学理论进行计算,但眼球看目标的距离发生变化时,其屈光度数也随之变化。
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