Serifs and font legibility

Abstract

Using lower-case fonts varying only in serif size (0%, 5%, and 10% cap height), we assessed legibility using size thresholds and reading speed. Five percentage serif fonts were slightly more legible than sans serif, but the average inter-letter spacing increase that serifs themselves impose, predicts greater enhancement than we observed. RSVP and continuous reading speeds showed no effect of serifs. When text is small or distant, serifs may, then, produce a tiny legibility increase due to the concomitant increase in spacing. However, our data exhibited no difference in legibility between typefaces that differ only in the presence or absence of serifs.

Full text

Serifs and font legibility
Aries Arditi
*
, Jianna Cho
Arlene R. Gordon Research Institute, Lighthouse International, 111 East 59th Street, New York, NY 10022, USA
Received 13 July 2004; received in revised form 8 June 2005
Abstract
Using lower-case fonts varying only in serif size (0%, 5%, and 10% cap height), we assessed legibility using size thresholds and
reading speed. Five percentage serif fonts were slightly more legible than sans serif, but the average inter-letter spacing increase that
serifs themselves impose, predicts greater enhancement than we observed. RSVP and continuous reading speeds showed no effect of
serifs. When text is small or distant, serifs may, then, produce a tiny legibility increase due to the concomitant increase in spacing.
However, our data exhibited no difference in legibility between typefaces that differ only in the presence or absence of serifs.
2005 Elsevier Ltd. All rights reserved.
Keywords: Legibility; Reading; Typography; Low vision
1. Introduction
It is well accepted that typeface affects text readability
(Mackeben, 1999; Mansfield, Legge, & Bane, 1996;
Roethlein, 1912; Tinker, 1963; Whittaker, Rohrkaste,
& Higgins, 1989), but apart from a few studies (Arditi,
1996; Arditi, Cagenello, & Jacobs, 1995a, Arditi, Cage-
nello, & Jacobs, 1995b; Arditi, Knoblauch, & Grun-
wald, 1990; Arditi, Liu, & Lynn, 1997; Berger, 1944a,
1944b, 1948) few experiments have addressed how care-
fully controlled, specific characteristics of font design
contribute to legibility. One reason for the paucity of re-
search in this area is that it is only since the advent of
computer fonts that it has it been reasonably easy to
construct fonts that can be varied parametrically. In-
deed, most studies assessing the impact of font charac-
teristics that use pre-existing fonts have difficulty
drawing definitive conclusions since virtually all such
fonts differ in more than a single characteristic (e.g.,
Mansfield et al., 1996; Yager, Aquilante, & Plass, 1998).
In the present study, we address the issue of how the
presence or absence of serifs contributes to readability
both at typical print sizes and close to the acuity limit.
To be able to draw firmer conclusions, we used fonts
of our own design that differ only in the presence or ab-
sence, and size of serifs. Since illegible typography ap-
pears to be a common complaint among people with
impaired vision, we also included two readers with
age-related macular degeneration (AMD) in our sample
of subjects. Given the small sample size, however, we
cannot draw firm or general conclusions about low vi-
sion from these data.
In the typographic literature, serifs are generally be-
lieved to have a significant impact on readability. There
are two main reasons cited to explain why serifs should
enhance legibility. First, they are believed to increase let-
ter discriminability by making the spatial code of letter
forms more complex. A well-known authority on typog-
raphy writes:
‘‘Sans-serif type is intrinsically less legible than ser-
iffed type...because some of the letters are more like
each other than letters that have serifs, and so the
certainty of decipherment is diminished.’’ (McLean,
1980)
0042-6989/$ - see front matter 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.visres.2005.06.013
*
Corresponding author. Tel.: +1 212 821 9500; fax: +1 212 751
9667.
E-mail address: aarditi@lighthouse.org (A. Arditi).
www.elsevier.com/locate/visres
Vision Research 45 (2005) 2926–2933

Second, serifs are thought to increase the visibility of
the ends of strokes, increasing the salience of the main
strokes of the letters Rubinstein (1988) writes:
‘‘Serifs have an important role in the readability of type,
providing...accentuation to the ends of strokes that
may help the reader read faster and avoid fatigue.’’
Serifs might thus enhance legibility of individual let-
ters by providing an additional cue to the location of
stroke ends.
A third possible reason, possibly implied by the
above quotation from Rubinstein, but not clearly artic-
ulated, is that those horizontal serifs that sit along the
font baseline might conceivably enhance the ability of
the reader to track the line of type with eye movements
and hence may promote faster or more efficient reading.
On the other hand, there are also good reasons to be-
lieve that serifs have little effect on legibility. Being small
relative to letter size, and generally being ornamental,
rather than essential parts of the letter form, one might
suspect that they would have little impact on letter iden-
tification. If they do affect legibility, it might be reason-
able to suppose that they interfere with letter
recognition, since to a simple letter-form template, they
might simply act as a form of noise.
Empirical studies, also, have shown that spatial fre-
quency information in letters, above 2–3 c/letter, is
unnecessary for letter recognition (Ginsburg, 1981),
and to support maximum reading speeds (Legge, Pelli,
Rubin, & Schleske, 1985). Since serifs are largely com-
prised of such high spatial frequency information, one
might suppose from these results, that they are irrele-
vant to legibility, especially at the acuity limit, where
spatial frequencies higher than 2–3 c/letter are likely to
be greatly attenuated by the optics of the eye.
Do fonts with serifs measurably enhance readabili-
ty? We sought to determine whether or not these tiny
features, which are clearly optional for basic letter
recognition, have positive, negative, or no impact on
legibility. Our criteria for demonstrating increased leg-
ibility were decreased size thresholds and increased
reading speeds. Since the addition of serifs to a font
increases the average inter-letter spacing of the font
slightly (to accommodate the serifs), we explicitly var-
ied inter-letter spacing as well, to independently assess
its effects. And since illegible typography is a common
complaint of people with low vision, we also included
two observers with age-related maculopathy in our
participant pool.
2. Methods
We assessed relative legibility of fonts with different
size (or no) serifs, and with different inter-letter spacing
using three different criteria for legibility:
1. Size thresholds (visual acuity) for letter identification,
measured with five-letter, random, lower-case strings
presented on a video monitor, using an up–down
staircase (Levitt, 1971) with 0.05 log unit size steps.
Size (or, inversely, distance) thresholds are probably
the most common method of assessing text legibility
(Tinker, 1963), and it is widely used in applied set-
tings such as highway signage, with lower size thresh-
olds indicating higher legibility.
2. Reading speeds using rapid serial visual presentation
(RSVP). More legible fonts, by this criterion, allow
faster reading, while less legible fonts prevent faster
reading. We measured reading speed using RSVP
with large letters (about seven times threshold size),
and conventional mixed-case text from an expanded
MNREAD (Legge, Ross, Luebker, & LaMay, 1989)
corpus. Reading speed is a less common measure of
legibility but it is perhaps more representative of
ordinary reading than is size threshold. And because
RSVP can support extremely high rates of reading, it
has the potential to be more sensitive to subtle differ-
ences in legibility. RSVP reading was tested with indi-
vidual sentences, whose speed was varied to
determine the speed that supported a 50% correct
reading rate.
3. Reading speeds using continuous reading of scram-
bled text passages using conventional text, printed
on paper. We included this condition to address pos-
sible differences between reading speeds with RSVP
on a computer monitor with those more commonly
observed with continuous reading on paper. We used
scrambled text to be able to compare performance on
three different conditions within subjects while using
text samples that have word frequency statistics that
are representative of ordinary text, but which require
reading of each individual word, rather than allowing
context and inference to play a significant role in
determining reading speed.
3. Stimuli
We constructed nine fonts using custom software
(Arditi, 2004) that allows parametric font construction.
Most of the font parameters are expressed as a proportion
of the cap height, which is the height of an upper-case let-
ter. The base font was constructed using strokes of uni-
form thickness that was 10% of the cap height. The
fonts had serifs whose strokes were of the same 10% cap
height thickness, and extended 0%, 5% or 10% of the
cap height. Each of these three serif sizes had space added
to their side bearings such that inter-letter spacing was
0%, 10%, or 40% of the cap height. This space was added
only at the edges of the letter glyph so that the letter shape
was unaltered by the manipulation of spacing. The full
alphabet is displayed for three sizes of serifs (0%, 5%,
A. Arditi, J. Cho / Vision Research 45 (2005) 2926–2933 2927

and 10% cap height) in Fig. 1, and the three spacing con-
ditions can be seen in Fig. 2. Other parameter values for
the font that were constant for the entire set of nine fonts
used in the experiment are: x-height: 55% cap height; and
descent: 50% cap height. Parameter values other than serif
size and spacing were chosen because they produce a rea-
sonably natural appearing font, but are otherwise arbi-
trary. Most important, they are the same for all
conditions of these experiments. In other words, the
shapes of letter glyphs were unchanged over all condi-
tions, except for the absence, presence, and size of serifs.
All other published studies that have examined the effects
of serifs have used existing, rather than custom fonts, and
none have been able to conclusively separate effects of ser-
ifs from other font design characteristics.
The nine fonts were used for all text employed in
these experiments, presented on both computer monitor
and paper.
3.1. Size thresholds
In this experiment, random five-letter strings were
presented centered on a SONY Multiscan 520GS moni-
tor, as black (3.6 cd/m
2
) letters on a white (129 cd/m
2
)
background. Normally sighted subjects viewed the
screen optically folded through a front-surface mirror
at an optical distance of 788.4 cm, so that letters were
at least 100 pixels in height (from the top of an upper-
case letter to bottom of the descent), or equivalently,
for these fonts, 66.66 pixels in cap height. For these sub-
jects, the letters were rendered in reverse on the screen to
compensate for the mirror reversal. Subjects with low vi-
sion viewed the screen directly (i.e., with no mirror) at
viewing distances of 106 (subject SM) and 58.4 cm (sub-
ject MG). The letter strings were sampled (with replace-
ment) from the 26 lower-case letters of the English
alphabet. Examples of such strings for the nine font con-
ditions are illustrated in Fig. 2.
3.2. RSVP reading
We used custom software to present each word of a
sentence centered vertically and horizontally on the
computer monitor, for a constant time interval. Text
was black on white, as with the size thresholds. The par-
ticipant read aloud each sentence as it was presented,
prior to presentation of the next sentence.
3.3. Continuous reading of scrambled text
Three text passages of roughly ninth grade-level read-
ing difficulty, and length 376, 400, and 405 words,
respectively, were used. The words of each passage were
randomly permuted, and printed on ordinary letter size
white paper, in 18 pt type. The subject read the text
aloud continuously, while the experimenter timed the
reading of the entire passage and recorded errors.
3.4. Participants
Normally sighted participants were Lighthouse re-
search staff (JC, CC), one of whom is an author of this
paper, or recruited from the Lighthouse International
Volunteer Service (AG, IF). Participants with low vi-
sion, both of whom had age-related maculopathy, were
recruited from the Lighthouse Low Vision Service (MG,
SM). MGÕs distance acuity, measured with a trans-illu-
minated Lighthouse/ETDRS distance acuity chart, was
1.0 log MAR (20/200), while SMÕs was 0.6 (20/80). Par-
ticipants were seated comfortably in a chair, with their
head position fixed with a head and chin rest. All partic-
ipants, except JC (who participated only in Experiment
1), were naı
¨ve to the purposes of the experiment.
4. Experiment 1: Size thresholds
4.1. Procedure
Size thresholds were measured using a staircase
method (Levitt, 1971) in which correct identification
Fig. 1. The full font (alphabetic characters) used in the study. The
letters are spaced with 10% cap height.
Fig. 2. Examples of lower-case fonts used in, and created for, the
experiment. Fonts differed only in size of serifs and by inter-letter
spacing. Both parameters are defined in units of percent of the height
of a capital letter in the font, which is also equal to the distance from
the top of a lower-case letter that has an ascending stroke, such as a
‘‘d,’’ to the font baseline.
2928 A. Arditi, J. Cho / Vision Research 45 (2005) 2926–2933

of at least four of five letters (in correct order) was re-
quired for a decrease in letter size on the subsequent
trial, while no more than three letters correct elicited
a size increase on the subsequent trial. This procedure
converges on the 68.6% correct point on the psycho-
metric function. Subjects were required to give five-let-
ter responses to all trials, and were encouraged to
guess if they reported difficulty. On trials in which
the size changed, the magnitude of the change was
0.05 log unit, half the size change from line to line
on state-of-the-art visual acuity charts. Data prior to
the 2nd reversal of each staircase were discarded, to
concentrate the data used in the analysis close to the
threshold.
To minimize sequence artifacts, the nine stimulus
conditions were randomly permuted once for each sub-
ject. First, that random sequence of nine conditions was
run in order, with each staircase terminating after 15
reversals. Next, the same sequence was run in reverse or-
der with each staircase terminating after 30 reversals.
Finally, the sequence was run in forward order again
with termination after 15 reversals. Thus, each condition
was run with a total of 60 staircase reversals, 30 in the
forward randomized order and 30 in the reverse ran-
domized order.
All responses were given verbally by the subject;
the experimenter typed the responses into the comput-
er, which then presented the next five-letter string
whose size was contingent on the subjectÕs perfor-
mance. Subjects were thus able to change their
responses if they did so prior to the experimenterÕs
finalizing the response to that line. This procedure re-
sults in a negligible lapse or extraneous noise rate
(Arditi, 2005).
4.2. Results
Size thresholds are shown as a function of serif size
and inter-letter spacing for the four normally sighted
participants in Fig. 3 and the two participants with
low vision in Fig. 4. These thresholds are geometric
means of all the staircase levels visited (after the sec-
ond reversal of each run); the number of measure-
ments on which the thresholds were based ranged
from 69 to 107. Standard errors (SEs) about these
means (which reflect accuracy of values in terms of
proportion, rather than magnitude) were small; the
maximum SE over all participants and all stimulus
conditions was 0.0026.
All of the plots slope downward as spacing increases,
indicating the presence of a large inter-letter spacing
‘‘crowding’’ effect, in which closely spaced letters result
in higher size (acuity) thresholds. Also evidents are
much smaller, but systematic effects of serif size on
threshold, with the threshold for the 5% serif nearly al-
ways being lower than that of the smallest (zero) serif
size. Averaged data are shown in Figs. 5 and 6, for nor-
mal and low vision, respectively, and in Fig. 7 for all
subjects. Note that the results are essentially the same
for the low vision subjects—those for whom, some
might argue, serifs should make a difference.
The above observations were corroborated with an
analysis of variance (ANOVA) performed on normal-
ized thresholds. First, so that data from the low vision
and normal vision groups could be combined, each sub-
jectÕs data were transformed by dividing each data point
by that subjectÕs minimum threshold, yielding a score
normalized to the subjectÕs best performance. The log
of this ratio was then used as the dependent variable
in an ANOVA with independent variables serif size, in-
ter-letter spacing, and vision status (normal or low), and
repeated measures on serif size, and inter-letter spacing.
The only significant effects were spacing (F[2, 8] =
143.888, p= 0.000) and serif size (F[2, 8] = 10.120,
p= 0.006).
Fig. 3. Letter size threshold as a function of inter-letter spacing and
serif size (squares: 0, circles: 5, and triangles: 10% cap height) for four
normally sighted participants. Serif size has a nearly negligible impact
on size threshold relative to spacing. Thresholds are plotted on log
axis.
Fig. 4. Same as Fig. 3 but for two observers with age-related
maculopathy. Note different scale from Fig. 3. Results are similar to
those of normally sighted observers.
A. Arditi, J. Cho / Vision Research 45 (2005) 2926–2933 2929

5. Experiment 2: Rapid serial visual presentation reading
5.1. Procedure
In this experiment, we assessed the affect of serif
size on reading using the RSVP reading technique.
This technique, in which words are presented one at
a time in the center of the computer monitor, allows
reading at higher speeds than with continuous verbal
reading (Rubin & Turano, 1994; Rubin & Turano,
1992), especially for normally sighted readers (Rubin
& Turano, 1992), and therefore might plausibly be
more sensitive to subtle differences in legibility. To
further enhance this sensitivity, we used sentences from
an expanded MNREAD corpus. These sentences are
by design 56 characters long (including interior spaces)
with comparable comprehensibility (See Mansfield,
Ahn, Legge, & Luebkerr, 1993 for details). Since the
sentences are very short, readers can store most or
all of each sentence in short-term memory, and report
the sentence verbally without needing to maintain a
high rate of verbal output, which might otherwise limit
speeds. Word presentation rate, which was controlled
by a desktop computer, was varied only between sen-
tences, by an amount that was contingent on reading
error rate.
We compared only the three fonts with 10% cap
height spacing using this technique, because we had a
limited number of 56-character MNREAD sentences
(357), and wanted to obtain error rates for a range of
presentation rates. Subjects were given practice on 60-
character MNREAD sentences prior to testing.
The experimenter determined informally during the
practice phase the speed region in which the subject be-
gan to make errors, by increasing speed by 20% if no er-
rors were made, and decreasing speed if errors were
made. Once data collection began, the speed increments
and decrements were reduced to 10%, and data collec-
tion proceeded in staircase fashion, such that if no errors
were made, the speed was increased; if no words in the
sentence were correctly identified, the speed was re-
duced. Our goal was thus to obtain nonzero error rates
for several presentation speeds, sampling a wide range
of the sloping portion of the psychometric function.
We obtained estimates of between 5 and 10 speeds for
each of the three conditions, for each subject. Error
rates (in characters per 56-character sentence) were then
fit by probit (Finney, 1971), to a cumulative Gaussian.
Maximum reading speed was taken to be the speed in
words per minute, at which 50% errors were made. Fol-
lowing the method of Carver (1976), speeds in words per
minute were computed by assuming that each sentence
was composed of 9.33 standard length words (each six
letters in length) and dividing by the exposure time for
the sentences.
Viewing distances and font sizes were chosen to
approximate an acuity reserve of about seven, easily en-
ough for comfortable reading (see Table 1).
Table 1
Viewing distance, font x-height, log minimum angle of resolution (log
MAR) and acuity reserve for the four participants of Experiment 2
Participant Viewing
distance (cm)
x-height
(cm)
log
MAR
Acuity
reserve
SM 50 2 0.6 6.9
MG 30 3 1.0 6.8
AG 100 0.9 0.1 7.8
IF 100 0.9 0.0 6.2
Fig. 7. Data of all subjects averaged (geometric mean) from Exper-
iment 1.
Fig. 5. Average (geometric mean) normal vision data from Experi-
ment 1.
Fig. 6. Average (geometric mean) low vision data from Experiment 1.
2930 A. Arditi, J. Cho / Vision Research 45 (2005) 2926–2933

5.2. Results
Fifty percent of correct RSVP speed thresholds for
the four participants reading the three fonts are shown
in Fig. 8. The data show no systematic effect of serif size
on reading speed. This was corroborated by a repeated
measures ANOVA, which resulted in no significant
effects.
Note the high reading speeds measured for normally
sighted subjects AG and IF. Very high speeds have pre-
viously been reported by Rubin and Turano (1992). Our
use of short sentences may have made such high rates
possible, since the reader could keep the entire sentence
in short-term memory prior to reporting it. Also, the
reading speeds we report (for computational conve-
nience) correspond to an estimated 50% character error
rate, which is a much higher error rate than would be
tolerated in ordinary reading.
6. Experiment 3: Continuous reading on paper
6.1. Procedure
Participants were given the scrambled reading pas-
sages and asked to read them aloud as quickly and accu-
rately as possible. The two subjects with low vision (MG
and SM) used their customary optical reading aids,
which were a 6·Eschenbach halogen illuminated stand
magnifier (MG) and a 4·Eschenbach torch hand mag-
nifier (SM). Participants were allowed to hold the pas-
sages in their hands, and no attempt was made to
control or advise reading distance. Reading of the pas-
sages was timed with a stop watch and errors recorded.
Credit was given for each whole word read correctly.
Reading speed was taken as the number of characters
within correctly read words divided by the time taken
to read the passage.
6.2. Results
Reading speeds, in characters per minute, are shown
for each subject in Fig. 9. Again, there are no systematic
differences in reading speed as a function of serif size,
and, as with RSVP reading, this was corroborated by
failure to find any significant effect in a repeated mea-
sures ANOVA.
7. Discussion and conclusion
In Experiments 2 and 3, the presence or absence of
serifs made no difference in reading speed, for all partic-
ipants, both normally sighted and those with low vision.
Only in Experiment 1, which used an acuity criterion of
legibility, was a statistical effect of serif size observed.
The size of the observed effect was extremely small, how-
ever. Looking at the average data of Fig. 7, the range of
the size threshold fell within 3.14 arc min (or about 0.11
of the threshold) for the zero spacing condition, 1.76 arc
min (0.08 threshold) for the 10 min spacing condition,
and 0.14 arc min (0.01 threshold) for the 40 min condi-
tion, with the intermediate (5% cap height) serifs yield-
ing the lowest thresholds, and highest legibility.
Note that a small degree of legibility enhancement
would be expected for serifs due to the increased letter
Fig. 8. RSVP reading speeds for 10% cap height letter spacing, as a
function of serif size. Speeds correspond to 50% error rate, as fit by
probit. Participants MG and SM have low vision, while IF and AG
have normal vision.
Fig. 9. Continuous reading speeds for text with 10% cap height letter
spacing, as a function of serif size. Participants MG and SM have low
vision, while IF and CC have normal vision.
A. Arditi, J. Cho / Vision Research 45 (2005) 2926–2933 2931

spacing that the addition of the serifs requires. In the
fonts used in the current experiment, 14 of 26 of the let-
ters have serifs along the baseline that add separation
between the letters. On average, the increased separation
is equal to 14/26 ·serif size. For the 5% serif font, the
increase in letter spacing is 2.69% cap height; for the
10% serif font, the increase is 5.38%. The average
slope of the linear segment between 0 spacing and 10%
cap height spacing is 2.56; that is, for each percent
cap height increase in letter spacing, threshold decreases
by 2.56 arc min. The 5% serif, then, should provide a
2.69 ·2.56 = 6.88 arc min reduction in size threshold,
while the 10% serif should result in a 2.56 ·5.38 =
13.77 arc min reduction, on the basis of increased letter
spacing alone. These reductions are far greater than
those observed, and therefore we conclude that, at least
at very small letter sizes, close to the acuity limit, serifs
may actually interfere ever so slightly with legibility.
This reduction is more than offset by an enhancement
of legibility caused by the increased spacing that results
from the addition of serifs, so the net effect is one of
slightly enhanced legibility for the intermediate (5% ser-
if) fonts.
This could also help explain why the slight enhance-
ment of legibility due to increased spacing due to serifs
is no longer seen in the 10% serif font, which has even
wider spacing. It is certainly plausible to posit that in
the case of the 5% serif, the serif and the additional let-
ter spacing required to accommodate it has a legibility-
enhancing effect that is stronger than any legibility-re-
ducing effect of the serif. But in the case of the 10% serif,
more inter-letter spacing does not outweigh the serifÕs
stronger legibility-reducing effect, perhaps because the
relief from crowding is greater when inter-letter separa-
tion is zero, while the serifÕs legibility-reducing effect
may be independent of spacing. The idea that serifs
might reduce legibility is also consistent with the recent
finding of Morris, Aquilante, Yager, and Bigelow
(2002), who found reductions in RSVP reading speed
with seriffed but not sans-serif type at sizes close to
the acuity limit (4 pt type at 40 cm), and not at larger
sizes.
We wish to offer three concluding caveats. First, we
have only studied a single font of our own parametric
design. It is possible that serifs in other fonts, especially
those designed with the critical eye of an expert font
designer, may have more of an impact. On the other
hand, while our font choices were to a degree arbitrary,
we can think of no reason why they would bias our re-
sults against finding stronger serif effects on legibility.
Second, we have used a small sample of participants.
It is certainly plausible that subtle differential legibility
effects of legibility could emerge from a larger study.
The present results are best taken to mean that substan-
tial legibility effects are absent; we can conclude little
about more subtle effects.
Third, while two subjects with AMD were included in
the participant sample, no firm or general conclusions
can be drawn about AMD or low vision, with respect
to font legibility. Again, if such effects exist, they are
either subtle enough to be undetected by our experimen-
tal methods, or they exist only within a subpopulation
not well represented by our two subjects with AMD.
In sum, we did find a small effect of serifs on size thresh-
olds, but it is unlikely to be of significance at typical print
sizes viewed under normal conditions. While subtle effects
on reading rate may emerge with larger subject samples,
the miniscule differences we found with this small sample
were apparent only with visually tiny print.
Acknowledgments
We thank Gordon Legge, Steve Mansfield, Beth
OÕBrien, and Lee Zimmerman for the expanded
MNREAD corpus used in this study, and Kathryn
Hargreaves for help with the font design, and two anon-
ymous reviewers for insightful comments. The work was
partially supported by NIH Grants EY12465, AG14586,
and EY015192, and grants from the Hoffritz and Pearle
Vision Foundations.
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