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Reference: Bio l. Bul l. 1 9 5: 1 4 .Aug ust , 1 9 98 )

Concepts in Imaging and M icroscopy

C hoosing O bjective L enses:

The Im portance of Num erical Aperture

and Magnifica tion

in D igital O ptical M icroscopy

DA VID W . PISTON

Dep artm en t o f Mo le cu la r Phy sio lo gy a nd B io ph ysic s V an de rb ilt Un iv er sity

Nashvi ll e Tennes se e 37232 -0615

A bstract. M icroscopic images are characterized by a

n um be r o f m ic ro sc op e-sp ec ific p ara me te rs n um eric al a p

erture (NA ), magnification (M ), and resolution (R)and

b y p ara meters th at a lso d ep en d o n th e sp ecim en for ex

am ple, co ntrast, sig na l-to -n oise ratio , d ynam ic rang e, an d

integration tim e. In this article, issues associated w ith the

m ic ro sc op e- sp ec if ic p ar am e te rs N A , M , a nd R a re d is cu ss ed

w ith respect to both w idefield and laser scanning confocal

m ic ro sc op ie s. A lth ou gh m o st o f th e d isc uss io n p oin ts a pp ly

to o ptic al m ic ro sc op y in g en er al, th e m ain a pp lic atio n c on

sidered is fluorescence m icroscopy.

Introduction

T he o bjectiv e len s is a rg ua bly th e m ost im po rtan t co rn

ponent of any light m icroscope (K eller, 1995). A dvances

in d igital im agin g have com pletely ch an ged the w ay th at

o ptical m icro sco py is p erfo rm ed , an d h av e also ch an ged

th e r ele va nt s pe cific atio ns fo r o bje ctiv e le ns es . A lth ou gh

len s d esign , constru ction, and qu ality have im proved to

keep up with the requirem ents of m odern light micros

copy, the markings on the lenses remain as they have

been for decades. O n the objective lens shown in Figure

Received13 February1998;accepted28 May 1998.

E-mail:[email protected]

T h is i s t he s ec on d i n a s er ie s o fa rt ic le s e nt it le d Conceptsn Imag ing

and Microscopy.This series is supported by the Opto-Precis ion Instru

ments Associa tion(OPIA)and was in troducedwith an editori al in the

A pr il 1 99 8 i ss ue o f th is jo ur na l (B io l. B ull . 1 94 : 9 9) . T he f irs t a rt ic le

in the seriesw as wr it tenby Dr . KennethR. Cas tl emanand appearedin

the same issue (Biol .Bull .194: 100107).

1, the w ord FLUARescrib es th e ty pe of len s d esig n;

although all m anufacturers use sim ilar types of designs,

the nom enclature varies from com pany to com pan y. T he

next most notable feature on the objective lens is the

m agnification (M ), w hich in the illustration is lO Ox. It

is w ritten in th e largest font of all the specification s, yet

as is discussed here, it is not the m ost im portant param e

ter. This distinction belongs to the num erical aperture

(N A), which is written next to the m agnification, but in

a smaller font, and in this case is 1.30. The imm ersion

m ed iu m for this objective is also given. B elow the m agn i

fica tion a nd n um erica l a pertu re, th e tu be len gth (00 ) a nd

th e co verslip th ick ness (0 .17 m m ) a re given . C urr en tly all

m anufacturers are offering infinity-corrected optics (de

noted by the oo sym bol), and m ost lenses are optim ally

corrected for a num ber 1.5 coverslip, nom inally 170-@ zm

thick. Both of these param eters are important, but the

objective lens w ill still function adequately for m any ap

plications w ith other tube lengths and coverslip thick

nesses. H owever, because the m anufacturers perform

ch ro ma tic co rrectio ns in d ifferen t w ay s, m ulti-c olor cx

p erim en ts fo r in sta nc e, c o-lo ca liz atio n o f tw o d iffe re nt

colored im munofluorescent probesshould be per

form ed using only sets of optics that were designed to

work together. This applies not only to m ixing lenses of

different m anufacturers, but also to m ixing older and

new er lines of optics. T he w orkin g d istan ce of the objec

tive (the depth into the sam ple to which the lens can focus

before it runs into the sam ple) is also a very im portant

param eter, especially for confocal m icroscopy in thick

b io lo gic al sam ples. D esp ite th e c ritical nature of th is sp ec

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D . W . P IST ON

ture are im portant for the im age-formation properties of

a n o ptic al m ic ro sc op e. M a gn ific atio n fo r a n o ptic al in str u

m en t is d efined as the relative enlargem ent of th e im age

over the object. Although at first glance it would seem

best to use the highest magnification possible, the maxi

m al useful m agnification is lim ited by the resolution of

the im aging instrum ent (as described in the next para

g ra ph ). T he d efin itio n o f n um er ic al a pe rtu re is m or e c or n

p lic ate d. N A is d efin ed b y th e h alf-a ng le o f th e o bje ctiv e s

collection cone (a) and the index of refraction of the

im m ersion m edium (n), and is expressed by N A =

n sin(a) (Inouand Spring, 1997, p. 32). The larger the

cone of collected light, the higher the NA, and the more

light that w ill be collected. Thus in practice, N A can be

thought of as the am ount of light that is collected by the

objective lens; a high-NA lens collects m ore light than a

low -NA lens. A n analogy is with telescopes: a larger

telescope collects m ore light just as a lens w ith a larger

N A collects more light. M ost optical m icroscopes also

offer the option of secondary m agn ification b etw een th e

ob jective len s and the detector. U se of such extra m agni

fication m ay som etim es be required (see Table I), but

should be avoided if possible since extra light loss is

introduced.

A s suggested above, resolution (as determ ined by the

b asic d iffr ac tio n p rin cip le s o flig ht) lim its th e u se fu l m ag

nification in an optical m icroscope. Resolution (R ) is de

fin ed a s th e sm allest d ista nce th at tw o o bjec ts ca n b e a pa rt

and still be discerned as two separate objects. There are

m an y m ath em atical d efin itio ns fo r resolutio n, b ut a sim ple

and reasonable approxim ation is R = X /(2 . N A), w here

x is thewav elengthfthelight(Inou ndSpring,1997,

p . 3 1). T his rela tio nsh ip in dica tes th at w hen u sin g a h ig h

N A lens and 500-nm (blue-green) light, the sm allest re

solva ble d ista nc e is @ 20 0rn, or 0.2 @ .tm ,w hic h a gr ee s

w ell w ith ex perim en ta l v alu es. O ne fr eq uen t p oin t o f co n

fusion for microscope users is the difference betw een

sp atia l reso lu tio n (th e a bility to d istin gu ish m ultip le o h

jects) and spatial precision (the ability to localize a single

object). M any im age-processing enhancem ents can be

used to increase the precision of localization. For exam

ple, the path of a single m icrotubule can be determ ined

to 10 nm precision by pixel-fitting (e.g., G hosh and

W ebb, 1994) or deconvolution methods (e.g., Agard et

al. 1989; Carrington et al. 1990; H olm es et al. 1995 .

H ow ev er, th is is n ot 1 0-n m reso lu tio n; 1 0-n m resolu tio n

m eans that two m icrotubules that are 10-nm apart can be

recogn ized as tw o sep arate tu bu les. If m ultiple objects

are sm all and close together (that is, close enough that

they cannot be resolved), then no am ount of image pro

cessing can differentiate betw een several individual oh

jects and a single object.

S in ce th ere is a m in im um reso lv ab le d ista nce fo r ev ery

m ic ro sc op e, c on tin uin g to in cr ea se th e m ag nific atio n p as t

a certain point will no longer increase the inform ation

O O @ @ 3o

1 j 0.17

@ -

fL-UAF@

Fig u re 1 . An o b je ct iv e l en s wi th t yp ic al m a rk in g s. Al th o ug h t hi s

i s a Zeiss lens ,m os tm anufac turersuse s imi la rmarkings .

ification, the w orking distance is not marked on m ost

lenses. Nikon has now started writing the working dis

tance on their CFI6O optics, and it is hoped that this trend

w ill be follow ed by th e other m an ufacturers.

This short article describes the relative im portance of

m ag nificatio n and n um erical ape rture fo r d ig ital op tical m i

croscop y. T rad ition ally, ob servation s m ad e w ith op tical m i

croscopes were detected by eye, and in this case, the size

o f th e d etecto r p ix els giv en b y p hy siolog ic al fa cto rs in

th e h um an e ye is n ot op tim al, so th e m ag nifica tio n w as

increased so the sam ple cou ld be seene tt er . I n d ig it al

im aging, how ever, the m agnification can be determ ined by

the com bin ation of resolu tion and detector p ixel size. To

u nd ersta nd th e rela tiv e im po rtan ce of N A a nd m ag nifica

tion, we m ust consider the basics of im age form ation and

th e e ffe ct o f le ns p ar am ete rs o n th e r es olu tio n a nd in fo rm a

tion content in optical m icroscopy. Because the resolving

pow er of an optical m icroscope is dependent only on the

num erical aperture, m agnification should be thought of as

a secon dary param eter w hose optim al value can be d eter

m ined by the N A, detector pixel size, and other instrum ent

independent im aging param eters. Thus, NA is a m ore im

portant parameter than m agnification in digital imaging.

T he p ra ctic al im p lic atio ns o f th is c on clu sio n a re d es cr ib ed

for two com monly used m odes of fluorescence im aging:

w id efie ld e pi-flu or esc en ce m ic ro sc op y w ith a C C D c am er a

as the d etector, and laser scann ing confocal m icroscopy

w i th photomult ip li er t ube de tect ors.

Basics of Image Formation

As m ight be guessed by looking at the m arkings on

any objective lens, the m agnification and num erical aper


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HOOSI NGOBJ ECTI VELENSES

(usually a CCD cam era) that takes the place of the eye.

T hus, to optim ize the inform ation content of the resulting

digital im age, the pixels on the detector m ust be m atched

to the desired im age resolution. A s describ ed above, th e

radius of a diffraction-lim ited spot, R@ X /(2 NA), is

a good quantity to use for the definition of resolution.

In the im age plane, this spot will still give the sm allest

resolvable object, but the w idth of the spot will now be

M . R . Based on the Nyquist criterion, the desired sam

pling rate should be twice the resolution, so we w ant a

pixel size in the object of R@ 1, R@ J2. In practice, the

p ixel size in w id efield m icro sco py is fix ed b y th e im ag in g

cam era used, so the m agnification is the only variable that

can be adjusted. For the purposes of these calculations,

we can assum e X = 0.5 @ tm(a good approxim ation for

fluorescein (FITC ) im aging). W e can determ ine the opti

m al M to be used for a given pixel size by m atching the

sam pling resolution in the im age plane to the pixel size

(P) by P = M . . Table I show s the results of this

calculation for tw o typical pixel sizes: 24 @ tm(an older

SITe 512D CCD chip) and 6.8 @ m(the m ore m odern

K odak KAF1400 CCD chip). As can be seen from the

tab le, the o ld er ch ip s (w ith the ir larg er p ix el size s) requ ire

higher m agnification. For these larger pixels, an extra

interm ediate m agnification of 2.5 w ould be required to

m axim ize the in form ation content of an im age collected

w ith a lOOx/l .3 N A objective lens, and in fact cam eras

that use the older SITe chip usually have som e extra

m agnification built into them . A s m icro-fabrication tech

n ology contin ues to ad van ce, how ever, the need for h igh

m agnification lenses will decrease. Obviously, it is not

possible to purchase a 72x/l.30 NA lens (although given

the popularity of the KAF1400 CCD chip, perhaps it

should be), so these optim al m agnifications can only serve

as a guide for selection of the best objective lens. Further

calculations, such as those presented in the table, reveal

that a cam era with a pixel size of 5.4 @ .tmwould be ideal

for use w ith m any existing lenses, such as 60x/l.4 NA ,

40x/0.90 N A, and 25x/0.60 NA. It should be noted,

however, that as pixel sizes get sm aller, the dynam ic

range of the detector m ay be reduced. For instance, the

5 .4 -@ .tmp ix els w ou ld lik ely b e fille d b y fe we r th an 2 0,0 00

counts, w hich w ould lim it the detector to 14-bit dynam ic

range. This is in contrast to larger pixel sizes (i.e., the

24 @ tmn the SITe 512D CCD chip), which can easily

deliver > 16-bit dynam ic range. For applications that

require high precision, such as deconvolution m ethods,

sm aller pixels m ay be unw orkable.

N u m er ic al a pe rtu re m a gn ifi ca tio n a nd r es olu tio n i n

la se r sc an nin g m ic ro sc op y

M uch has been m ade of the im provem ent in resolution

provided by confocal m icroscopy. B ut this im provem ent

is at best m inim al, and is only attained for extrem ely

content of the im age. Further m agnification beyond this

point is som etim es referred to as emptyr meaningless

m agnification. This is analogous to any digital im age on

a com puter, w here pixelation is observed w hen an im age

is m agnified on the screen (this can be seen, for exam ple,

by repeatedly using the z oo mn c om m an d in A do be

P ho to sh op ). S o th e q uestion o bv io usly a rises, h ow sh ou ld

the correct m agnification be chosen? A good rule is to

use the N yquist criterion, which basically says that one

should collect tw o points per resolution size (Inou and

Spring, 1997, p. 513). Collecting im ages in this m anner

m axim izes the in form ation con ten t.

The use of XI(2 . NA ) for the resolution criterion, and

of R /2 for the sampling rate are both arbitrary. M any

m icroscopists select other resolution criteria, but all of

these choices are only m athem atical approxim ations of

the sam e physical properties. U se of any other resolution

criteria w ould not affect the argum ents presented here,

a lth ou gh th e n um bers (e.g ., th ose sh ow n in T ab le I) w ou ld

c ha ng e s lig ht ly .

Som e atten tion should also be given to special con sid

erations for fluorescence m icroscopy (R ost, 1992). Since

fluorescence is subject to fluorophore saturation and pho

tobleaching effects that do not affect other optical m eth

ods, the highest possible light collection efficiency is de

sirab le. T his co nside ratio n d ictates th at th e h ig hest po ssi

ble N A should be used. However, the highest NA lenses

(N A = 1.40) are usually of a plan-Apochrom at esign;

this type of lens consists of up to 14 elem ents and has a

lo we r tr an sm itta nc e th an a Fluoresign. A lso, if aq ue

ous sam ples are used, the actual N A is lim ited to @.2

because of total internal reflection for higher collection

a ng le s a t th e in te rfa ce b etw ee n w ate r a nd c ov er slip (I no u

a nd S pr in g, 1 99 7, p p. 5 3 55 ). Fo r th ese r ea so ns, flu or es

cence from an aqueous sam ple appears brighter through

a 100x/l.30 N A FLUA R (as shown in Fig. 1) than

through a lO Ox/1.40 plan-A pochrom at objective lens.

Finally, it should be noted that im provem ents in alm ost

every aspect of lens design and construction (e.g., corn

puter design of com plex lens com bination, autom ated

grinding of arbitrary lens shapes, new optical m aterials

fo r b oth len ses an d coa tin gs, and co mp uter-con tro lled th in

film d ep osition for p recise o ptical co atin gs) m ak e m odern

objective lenses superior to and m ore reliable than older

lenses. A lthough m any older lenses are superb, variables

during their construction m ad e find in g a good one som e

w hat challenging, and m any researchers just took what

cam e. Today s lenses are consistently of high quality,

and also offer higher transm ission efficiency and low er

autofluorescence than did older lenses.

N u me ric al a pe rtu re m a gn ifi ca tio n an d r es olu tio n i n

wide fi el d m i croscopy

In a digital w idefield (conventional fluorescence) m i

croscope, the im age is projected onto an im aging detector


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Numerical apertureNA)1.401.300.900.600.30Calculated

resolutionsam)Rdjff0.180.190.280.420.831L,,0.0900.0950.1400.2100.415Magnification

(x)24-jim

pixels*267253171114586.8-jim

pixelst7672493216

4 D. W . PISTO N

T abl e I

Optima l magni fica tionfor de tec to rs wi th d i ffe ren tp ixel s ize s ca lcu la ted for f ive numer ica l aper tures

Represents the SITe5 l2D CCD chip.

t Representshe KodakKAF1400CCDchip.

sm all p in holes. In p rac tical flu orescen ce m icro scop y, th e

pinhole m ust be opened som ewhat to increase the effi

ciency of fluorescence collection. In fact, the pinhole is

alm ost always opened enough to negate any resolution

enhancem ent (Sandison et al., 1995). In this practical

ca se, th ere is a n im prov em en t in rejectio n o f o ut-o f-fo cu s

background, but the resolution is still given by R@

(2 N A), so the ideal sam pling resolution rem ains as show n

in Table I.

A key point in laser scanning m icroscopy is that there

is no longer a fixed pixel size. Because the field over

which the laser is scanned can be varied (this variation

is usually called zoom,r m ore appropriately elec

t ron ic zoom, nd is analogous to using an optical zoom

len s), the sam plin g resolution can b e easily changed . F or

this reason, users often have a lot of trouble choosing

lenses w hen they switch to laser scanning confocal m i

croscopy. For instance, a 40x lens w ith a zoom factor of

2.5 is basically equivalent to a lO O x lens with no extra

zoom . Thus, a 40x/1 .3 NA lens should be chosen over

an equivalent lO Ox/1.3 N A lens, because it offers a poten

tially larger field of view w ith no fall-off in light collec

t io n o r r es olu tio n.

In laser scanning confocal m icroscopy, tw o other pa

ra meters m ust b e co nsid ered . F irst is th e size of th e d etec

tor pinhole, which depends on the m agnification. M ost

confocal m icroscopes have an adjustab le pinhole that is

easily set to m atch the m agnification (e.g., for equiva

lence, a 60x lens needs a pinhole 1.5-fold larger than a

4 0x len s). S eco nd ly , th e len s d esig n fo r co nfo cal m icro s

copy m ay, in som e cases, be m ore im portant than either

M or N A. T his is esp ecia lly tru e fo r co -lo caliza tio n ex per

im ents, in which the chrom atic corrections of a plan

Apochrom at make it preferable despite its lower light

co llectio n efficien cy (th e sam e tra de-o ff m ust b e co nsid

ered for any three-dimensional microscopies based on

w id efield an d decon volu tion m eth od s, as w ell). R egard

less of the lens design, how ever, a lower m agnification

lens (of equivalent N A) is alm ost always preferable, be

cause it offers a larger field-of-view , and delivers equiva

l ent resolut ion.

Acknowledgments

This work w as supported by an Arnold and M abel

Beckm an Foundation Y oung Investigator A ward, NIH

grant DK 53434, and the Vanderbilt Cell Im aging Re

source (underw ritten by C A68485 and D K20593).

L ite ra tu re C ite d

A g ar d, D . A . , Y . H lr ao ka , P . S ha w , a nd J . W . S ed at. 1 98 9. F lu or es

cence m icro sco py in threedim ensions .Metho dsCe l l B iol . 3 0 : 3 5 3

377.

C arrln gto n, W . A . , K . E . F og arty , a nd F . S . F ay . 1 99 0. 3 D f lu ore s

c en ce i m ag in g o f s in gl e c el ls u si ng i m ag e r es to ra ti on . P p. 5 3 72n

N on invasive T echniques in C ell B iology. J. K . F oskett and S.

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Ghosh, R. N., and W . W . W ebb. 1994. Autom ated detection and

trackingof individualand clusteredcellsurfacelow densitylipopro

t ei n r ec ep to r m o le cu le s. B io ph ys . J . 6 6: 1 30 1 138 .

H olm es, T . J., S . B hattac ha ry ya , J. A . C oo per, D . H an zel, V . K rlsh

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t al s 2n d E d it io n. P le nu m N e w Y o rk .

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choosing objective lenses

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