Physiological optics in the hummingbird hawkmoth

The Journal of Experimental Biology 202, 497–511 (1999)
Printed in Great Britain © The Company of Biologists Limited 1999
of Zoology, University of Lund, Helgonavägen 3, S-22362 Lund, Sweden, 2Institute for Advanced Study,
Wallotstrasse 19, D-14193 Berlin, Germany and 3Lehrstuhl für Biokybernetik, Universität Tübingen, Auf der
Morgenstelle 28, D-72076 Tübingen, Germany
*e-mail: [email protected]
‡Present address: Public Communication Networks Group, Siemens AG, Siemensdamm 50, D-13623 Berlin, Germany
Accepted 7 December 1998; published on WWW 3 February 1999
angular packing of the overlying corneal facets. In fact, this
The fast-flying day-active hawkmoth Macroglossum
eye has many more rhabdoms than facets, with up to four
stellatarum (Lepidoptera: Sphingidae) has a remarkable
rhabdoms per facet in the frontal eye, a situation which
refracting superposition eye that departs radically from the
means that M. stellatarum does not possess ommatidia in
classical principles of Exnerian superposition optics.
the accepted sense. The size of the facets and the area of
Unlike its classical counterparts, this superposition eye is
the superposition aperture are both maximal at the frontal
highly aspherical and contains extensive gradients of
retinal acute zone. By having larger facets, a wider
resolution and sensitivity. While such features are well
aperture and denser rhabdom packing, the frontal acute
known in apposition eyes, they were thought to be
zone of M. stellatarum provides the eye with its sharpest
impossible in superposition eyes because of the imaging
and brightest image and samples the image with the densest
principle inherent in this design. We provide the first
photoreceptor matrix. It is this eye region that M.
account of a superposition eye where these gradients are
stellatarum uses to fixate flower entrances during hovering
not only possible, but also produce superposition eyes of
and feeding. This radical departure from classical
Exnerian principles has resulted in a superposition eye
ophthalmoscopy, we find that superposition images formed
which has not only high sensitivity but also outstanding
in the eye are close to the diffraction limit. Moreover, the
spatial resolution.
photoreceptors of the superposition eyes of M. stellatarum
are organised to form local acute zones, one of which is
frontal and slightly ventral, and another of which provides
improved resolution along the equator of the eye. This
Key words: hummingbird hawkmoth, Macroglossum stellatarum,
superposition eye, compound eye, diffraction limit, optics, vision.
angular packing of rhabdoms bears no resemblance to the
The hummingbird hawkmoth Macroglossum stellatarum is
one of Europe’s most delightful insects. Active almost
exclusively in bright daylight, this moth is not only a fast and
aerobatic flier but also an excellent hoverer, sucking nectar
from flowers in much the same way as its namesake the
hummingbird. Its visual behaviour has been the subject of
study since the early part of this century (Knoll, 1922), more
recently with regard to visual stabilisation of flight (Kern,
1994, 1998; Kern and Varju, 1994, 1998; Farina et al., 1995),
distance perception (Pfaff and Varju, 1991; Farina et al., 1994),
colour vision (Kelber, 1996; Kelber and Henique, 1999) and
flower recognition (Kelber, 1997; Kelber and Pfaff, 1997).
Whilst much information has been obtained regarding the
visual behaviour of M. stellatarum, very little is known about
its eyes.
There are many paradoxes associated with the eyes of M.
stellatarum. First, despite being day-active, it has superposition
eyes with well-developed tapeta, a compound eye design more
typical of insects active at night. Second, the eyes are
extremely aspherical and inhomogeneous, and thereby fail to
adhere to the accepted optical construction necessary to form
a superposition image on the retina. In the accepted model, first
developed by Sigmund Exner over 100 years ago (Exner,
1891), superposition eyes are spherical and maintain a constant
focal length and angular magnification throughout the eye.
Most superposition eyes conform more or less to this classical
In a future publication (E. Warrant, K. Bartsch and C.
Günther, in preparation), we will show that the eyes of M.
stellatarum not only form crisp superposition images but also
possess the sharpest angular sensitivities yet known for a
superposition eye. In the present study, we take a closer look
at the optics of the eye in an attempt to understand how Exner’s
rules can be broken and still permit excellent superposition
vision. In attempting to unravel this paradox, we discovered
that the eye had two remarkable properties. First, as in many
apposition eyes, there are gradients of resolution and
sensitivity throughout the eye. Gradients in resolution were
previously deemed impossible for superposition eyes. Second,
there is not one corneal facet per rhabdom as in a conventional
compound eye, but as many as four, the exact ratio depending
on the location in the eye. Because an ommatidium contains
one rhabdom and one facet, this means that M. stellatarum
does not have ommatidia in the functional sense, and the
concept of an interommatidial angle is meaningless. The eyes
of M. stellatarum represent a remarkable optimisation of the
superposition design for vision in bright light, and their
physiological optics are described here for the first time.
An abstract of this work has been published previously
(Bartsch and Warrant, 1994).
Materials and methods
Macroglossum stellatarum L. (Lepidoptera: Sphingidae)
was reared in a laboratory culture that was regularly restocked
with wild-caught moths from Southern Europe. Full details of
the rearing and maintenance of hummingbird hawkmoths can
be found elsewhere (Farina et al., 1994).
All visual field coordinates used in this study comply to the
conventions given in Fig. 1. Angles of latitude and longitude
were defined with the origin (0 °,0 °) located at the lateral (side)
point of the eye (L). Longitudes anterior (A) to this point are
positive, those that are posterior (P) are negative. The same
convention applies to latitude: latitudes dorsal (D) of the lateral
point are positive, those that are ventral (V) are negative.
Corneal measurements of eye glow area, facet diameter and
inter-facet angle were made using a large goniometer together
with a low-power microscope whose objective could be placed
at any position on the surface of an imaginary hemisphere
centred on the eye of a living hawkmoth. Attached to the
microscope was a camera. The hawkmoth was restrained
within an Eppendorf tube whose tip had been sliced off to
allow the moth’s head to protrude. The head was lightly fixed
to the tube with a small quantity of beeswax to prevent it from
moving. Excess scales and hairs were carefully plucked from
the head to allow a full view of the eye. Chalk dust was then
sprinkled lightly onto the eye to provide landmarks. A mount
holding an oriented glass coverslip was then placed over the
end of the objective. This coverslip, oriented at 45 ° to the
objective’s long axis, acted as a beam splitter which diverted
orthodromic light from a small lamp, placed to the side of the
objective, down onto the eye. This light caused a bright eye
glow which could be seen through the microscope. The details
Fig. 1. The coordinate system used in this study. The origin (0 °,0 °)
was defined at the lateral point (L) of the eye, and angles of latitude
and longitude were defined in the manner shown. D, dorsal; V,
ventral; A, anterior; P, posterior.
and operation of the goniometer are described by Dahmen
The experimental procedure was as follows. The goniometer
was used to move the microscope through steps of 10 °
longitude. At each longitude, the microscope was moved
through steps of 10 ° latitude, beginning as far ventrally as
possible and progressing dorsally until the microscope had no
further travel. At each position, the eye glow was
photographed, and the photographs were used to determine the
size, shape and facet content of the eye glow. Facet diameter
was also determined at each position. On the basis of the
number of facets traversed by the eye glow during the 10 °
transition from one photograph to the next, it was possible to
measure the angle separating neighbouring facets at each eye
position (using a method analogous to that used by Horridge,
1978, and Dahmen, 1991, in apposition eyes).
Retinal measurements of line-spread functions, point-spread
functions and the angular packing density of rhabdoms were
made using ophthalmoscopic techniques (for a full
explanation, see Land, 1984a). These methods allow the retina,
and any images formed on it, to be viewed through the eyes’
own optics. A short description of the principal methods used
will be given below. Specific details of some procedures – best
explained in the context of the Results – are given at the
appropriate places in the Results section.
For measurements of the packing density of rhabdoms, the
Physiological optics in the hummingbird hawkmoth
ophthalmoscope was a converted Zeiss photoscope. This
contained a half-silvered mirror which diverted light from a
laterally placed light path through the objective (Fig. 2). The
light was produced by a xenon arc lamp and filtered by an
interference filter transmitting light in the wavelength range
550–650 nm. Hawkmoths, restrained as described above, were
placed on a small goniometer that could be used together with
the rotating microscope stage to position the moth at a chosen
latitude and longitude under the objective. A Bertrand lens
inserted into the beam path (Fig. 2) allowed the retina to be
viewed in angular space. Slits, pin-holes, letters and gratings
placed at the position of the angular diaphragm could then be
imaged on the retina. Images so produced could be intensified
by an image intensifier, collected by a CCD camera, enhanced
with an electronic image-analysis system and printed on a
video printer. Removal of the Bertrand lens allowed the
corneal surface to be viewed.
For optical measurements of rhabdom acceptance functions,
the ophthalmoscope was a bench-mounted arrangement of
Spindler and Hoyer optical components (for a full description,
see Land, 1984a). Images were photographed with an Olympus
OM-2 camera using Kodak TMAX400 black-and-white slide
film and developed in TMAX developer. The resulting
negatives, which contained an intensity range of over 3
logarithmic units (sufficient for quantitative microdensitometry), were illuminated from below by a 0.075 mm
wide circular pin-hole of light. Densitometry was performed
by reading the voltage output of a photodiode placed above the
negative as the light source was moved beneath the negative
in 0.05 mm steps. To convert voltage readings into intensities
and to standardise readings between different films, a slide
made up of strips of known neutral density (strips made from
gelatin) was photographed on every film. This slide provided
the calibration curve for the film.
Electron microscopy
Whole eyes were placed for 2 h at 4 °C in standard fixative
(2.5 % glutaraldehyde and 3 % paraformaldehyde in
150 mmol l−1 sodium cacodylate buffer, pH 7.2). Following a
Fig. 3. The eye of Macroglossum stellatarum in
horizontal section. This longitudinal view, in the plane of
the eye’s equator, very clearly shows the highly nonspherical nature of the eye. Because neither the retina (r)
nor the cornea (c) is spherical or concentric, the clear
zone of the eye (cz) varies in size throughout the eye. The
lamina (l) and medulla (m) of the optic lobe are also
visible. a, anterior; p, posterior. Scale bar, 200 µm.
lamp Shutter
Spectral Lens
with animal
Fig. 2. The ophthalmoscopic apparatus. A converted Zeiss
photoscope, containing a half-silvered mirror, diverted light (600 nm,
∆λ=100 nm) from a xenon arc source to the eye of a hawkmoth
placed on a goniometer beneath the objective. Placement of a
Bertrand lens in the beam path allowed the retina to be imaged. Slits,
pin-holes, letters and gratings placed at the position of the angular
diaphragm could then be imaged on the retina. Images could be
intensified, captured by a CCD camera and printed on a video
printer. A regular camera could also be used in place of the
intensifier and CCD camera.
rinse in buffer, the eyes were added to 1 % OsO4 for 1 h.
Dehydration was performed in an alcohol series, and the eyes
were embedded in Araldite. Ultrathin sections for electron
microscopy were stained with lead citrate and uranyl acetate.
An aspherical superposition eye
The refracting superposition eye of M. stellatarum is highly
aspherical (Fig. 3), and ommatidial anatomy and optics vary
throughout the eye. The aspherical nature of the eye is clearly
seen in horizontal (equatorial) longitudinal sections (Fig. 3).
Neither the corneal surface nor the retinal surface is concentric
or spherical, and the size of the clear zone and the lengths of
the rhabdoms vary throughout the eye. In this respect alone,
the eyes depart radically from the classical Exnerian norm of
sphericity and homogeneity. As we shall see, this departure
also extends to other aspects of the eye. Despite this, angularsensitivity functions with acceptance angles as small as 1.3 °
can be recorded from the photoreceptors, indicating that image
quality on the retina is very good (the anatomy and physiology
of the eye will be expanded upon by E. Warrant, K. Bartsch
and C. Günther, in preparation).
Optical image quality
To assess image quality, we used the ophthalmoscopic
techniques pioneered for insect eyes by Land (1984a). These
methods allow the retina, and any images formed on it, to be
viewed through the eyes’ own optics. One way of assessing the
optical quality of the eye is to use the ophthalmoscope to look
at retinal structures, such as the array of photoreceptors. If the
array is clearly visible, the optical quality is good. Because the
image we see has passed only once through the optics of the
eye (outwards from the retina), any measurements made from
these images are referred to as ‘single-pass’. An alternative
way of assessing the optical quality is to place objects (such
as points, lines and gratings) outside the eye and then examine
their images on the retina. Such measurements are ‘doublepass’ because light from an object is imaged twice by the
optical system: once on its way to the retina, and once again
on its way back out. The image of relevance to the animal is
that formed on the inward journey to the retina: the single-pass
image. Luckily, any double-pass images we capture in the
ophthalmoscope can be converted to single-pass images using
standard procedures (which are very clearly explained by
Land, 1984a).
As a qualitative indication of image quality in M.
stellatarum, we projected letters and square-wave gratings
Fig. 4. Ophthalmoscopic images of the retina in Macroglossum
stellatarum; lateral eye (0 °,0 °). (A) The clearly visible matrix of
rhabdoms. (B) A musical ‘natural’ sign (height 18.4 °) imaged on the
retina. The original object was placed in the plane of the
ophthalmoscope’s angular diaphragm (see Fig. 2). Scale bar (for
both parts), 4 °.
onto the retina using the ophthalmoscope (Figs 4, 5). The
retinal photoreceptor array of the lateral eye (0 °,0 °; see Fig. 1)
was clearly visible (Fig. 4A), indicating that the eyes are well
focused. It also indicates that the quality of the optical system
in this part of the eye is better than the retinal ‘grain’, i.e. that
the angular separation of neighbouring rhabdoms (∆φ) is
greater than the angular half-width (in object space) of the
receptive field of each rhabdom (∆ρ). According to Land
(1984a), the photoreceptor array will only be visible when ∆φ
exceeds 0.9∆ρ. In the lateral eye ∆φ≈2.0 ° and ∆ρ≈1.8 ° (see
below), so this indeed seems to be the case. In this regard, M.
stellatarum can be compared with two other diurnal
lepidopteran species (measurements made by Land, 1984a):
the eyes are at least as well focused as those of the agaristid
moth Phalaenoides tristifica and somewhat better focused
than those of the skipper butterfly Ocybadistes walkeri.
Interestingly, in the frontal part of the retina of M. stellatarum,
the packing of the rhabdoms becomes much denser and the
ophthalmoscope can only just resolve the photoreceptor array.
It seems that in this part of the retina ∆ρ approaches or is
slightly larger than ∆φ. This notion is supported by
electrophysiological measurements of ∆ρ (1.3–1.4 °: E.
Warrant, K. Bartsch and C. Günther, in preparation) and
optical measurements of ∆φ (approximately 1.1 °; see below).
Double-pass images of objects placed outside the eye are
Fig. 5. High-contrast square-wave gratings of various angular
periods imaged on the equatorial frontal retina (longitude 70 °).
(A) 12 ° period (0.08 cycles degree−1); (B) 8 ° period
(0.13 cycles degree−1); (C) 6 ° period (0.17 cycles degree−1); (D) 4 °
period (0.25 cycles degree−1). All gratings are clearly resolvable on
the retina, except the 4 ° grating whose contrast has declined
markedly. Scale bar (for all parts), 5 °.
Physiological optics in the hummingbird hawkmoth
also clearly visible, with a musical ‘natural’ sign of 18.4 °
height being easily seen (Fig. 4B). When high-contrast squarewave gratings are projected (Fig. 5), those of lowest spatial
frequency (0.08 cycles degree−1) are easily resolved (Fig. 5A),
although the sharp edges of the grating object are lost in the
image (due to diffraction). Gratings are still very clear even at
0.17 cycles degree−1 (Fig. 5C), but by 0.25 cycles degree−1 they
are difficult to discern (Fig. 5D).
Quantitative measurements of optical quality can be made
by optically measuring the acceptance functions of single
rhabdoms. This was performed by observing the image of a
0.49 ° point source centred on a single rhabdom in the lateral
eye (Fig. 6, inset) and measuring the distribution of light in this
image using densitometry. Whilst almost all of the light in the
photographed image arises from the single central rhabdom,
some light does arise from the neighbouring six rhabdoms.
Because the light is emitted through the same aperture from
which it entered, the resulting light distribution should be
identical to the rhabdom’s acceptance function whose halfwidth is ∆ρ (the acceptance angle). Moreover, this distribution
should also be ‘single-pass’ because a single rhabdom accepts
and emits almost all of the incoming point source blur-circle.
Note that the image shown in the inset of Fig. 6 is somewhat
elliptical, a phenomenon that is often encountered. Acceptance
functions were measured by making a densitometric scan along
the long axis of the elliptical image. The scan appears roughly
Gaussian (circular symbols in Fig. 6) and, in fact, can be
Relative intensity
Angle (degrees)
Fig. 6. The acceptance function of a single rhabdom in the lateral eye
(0 °,0 °) of Macroglossum stellatarum measured optically from the
image of a point source on the retina (inset). Point-source images,
which were essentially single-pass (see text), were generated by
centring the image of a pin-hole of light (0.49 ° wide) on a single
rhabdom. Experimental data (circles) were obtained from several
densitometric scans across the image shown in the inset. A
theoretical acceptance function (heavy continuous line) was then
derived by fitting these data to equation 1 (see text). This function, of
half-width 1.81 °, fits the data better than a single Gaussian function
of the same half-width (thin continuous line). The inset image
measures 4 °×4 °.
accurately fitted by a function R(θ) composed of the sum of
two Gaussian functions, one having a higher amplitude and
narrower half-width, and the other having a lower amplitude
and broader half-width:
θ 2 + A exp − ––
θ ,
R(θ) = A1exp − ––
冤 冢 冢冤
冤 冢 冢冤
where θ is a variable (angle), A1, a1, A2 and a2 are constants
and A1+A2=1. The half-width hi of each Gaussian function is
related to the constant ai (the ‘natural radius’) via the simple
relationship ai=0.6hi. The receptive field data shown in Fig. 6
can be accurately fitted by equation 1 with the following bestfit constants: a1=0.89 °, A1=0.621, a2=1.65 ° and A2=0.379
(correlation coefficient r2=0.98). The half-width of the total
function is 1.81 °. The data can almost be fitted by a single
Gaussian function of the same half-width (thin inner profile in
Fig. 6), but the data points lie above the flanks of this profile.
This is the ‘image flare’ we observed in the photographed
image (Fig. 6 inset). Whilst not extremely large in M.
stellatarum, it does have the potential to reduce image contrast
significantly and thus to make vision worse (Land, 1984a).
Interestingly, exactly the same thing is seen in
electrophysiologically measured acceptance functions (E.
Warrant, K. Bartsch and C. Günther, in preparation), implying
that these flanks have a real effect on cellular receptive fields.
The acceptance functions of rhabdoms in the lateral eye thus
have acceptance angles (∆ρ) of 1.81 °. Knowing this angle also
makes it possible to estimate the half-width ∆ρl of the blurred
point source image (or blur-circle) formed on the retina. The
acceptance function is the mathematical convolution of the
blur-circle and the circular top-hat function representing the
stop at the tip of the rhabdom. This stop is defined by the
cylindrical sheath of tracheal tubes that surrounds each
rhabdom and internally reflects light from the blur-circle into
the rhabdom (Land, 1984a; Warrant and McIntyre, 1991; E.
Warrant, K. Bartsch and C. Günther, in preparation). Using a
method described by Land (see Land, 1984a, Fig. 9), it is
possible to derive ∆ρl from ∆ρ and the angular width of the
stop (∆ρr). In the lateral eye of M. stellatarum, ∆ρr≈1.73 °.
With ∆ρ=1.81 °, this gives ∆ρl=1.27 °.
How does this value of ∆ρl compare with the value expected
if the blur-circle quality was limited only by the diffraction of
light at each corneal facet? Images formed by an optical system
can never be sharper than this diffraction limit. In a diffractionlimited eye, ∆ρl=180λ/πD, where λ is the wavelength of
incoming light and D is the diameter of a single facet (Land,
1981). In the lateral eye of M. stellatarum D=29 µm (see
Fig. 8). Taking λ=0.6 µm (the median wavelength used during
these experiments) gives ∆ρl=1.19 °. This is narrower than our
experimental value of 1.27 ° by 0.08 °, implying that the lateral
eye of M. stellatarum, whilst being close to the diffraction
limit, may suffer very slightly from image-degrading
aberrations. Diffraction-limited superposition eyes have been
found in the diurnal agaristid moth Phalaenoides tristifica, but
in the diurnal skipper butterfly Ocybadistes walkeri the
hovering (not shown in Fig. 8). In more posterior regions of
the eye, the facets lose their perfect hexagonal shape and
become compressed in the anterior–posterior direction
(Figs 7A, 8B). In the dorso-ventral direction, facets are largest
and most hexagonal at the equator, reaching diameters of
approximately 29 µm (Fig. 8A). Both above and below the
equator, facets become smaller but remain fairly hexagonal.
Eye glow
The superposition eye of M. stellatarum possesses a
reflective tapetum, which lies in the retina. Light rays that have
not been absorbed within the eye can be reflected by the
tapetum and returned to a distant observer through the same
aperture of facets as they entered. If the eye is illuminated and
viewed coaxially with the illumination (i.e. orthodromic
illumination), a bright patch of blue-green light can be seen on
the eye surface (E. Warrant, K. Bartsch and C. Günther, in
preparation). This patch, called the eye glow, represents the
pupil through which light reaches the retina: a larger eye glow
represents a larger pupil and a greater light catch. In most
nocturnal superposition eyes, a bright eye glow is usually
associated with a dark-adapted and fully open pupil. Continued
illumination of such an eye normally causes screening
pigments within the eye to migrate and ‘close’ the pupil. The
eye glow then fades. Remarkably, in many diurnal
superposition eyes including those of M. stellatarum, the pupil
is always fully open, as if in the dark-adapted state, even
though the animals themselves fly only in bright sunshine (E.
Warrant, K. Bartsch and C. Günther, in preparation). The pupil
can be partially closed, but only using unnaturally bright light
(Warrant and McIntyre, 1996; E. Warrant, K. Bartsch and C.
Günther, in preparation). The significance of this is not
understood at present.
Fig. 7. The facet matrix at two different equatorial locations:
longitudes −15 ° (A) and +60 ° (B). The top, bottom, left and right
edges of each panel represent the dorsal, ventral, posterior and
anterior directions respectively. Facets are larger and more regularly
hexagonal at the front of the eye (B). Scale bar (for both parts),
30 µm.
superposition eyes are somewhat worse than the diffraction
limit (Land, 1984a). M. stellatarum lies somewhere in
between, but closer to Phalaenoides than to Ocybadistes.
Corneal facet diameter
The corneal facets of M. stellatarum maintain neither a
constant diameter nor a perfectly hexagonal shape throughout
the eye (Figs 7, 8). This is not uncommon in many apposition
eyes, but for superposition eyes it is very unusual.
Facets are largest and most hexagonal in the anterior part of
the eye, with diameters exceeding 30 µm along the equator at
longitudes around 60 ° (Fig. 8B). For longitudes further
anterior, the facets maintain this shape and maximum diameter
ventrally of the equator, notably in the region of the eye used
by M. stellatarum to fixate the entrance of a flower during
Facet diameter (µm)
-100 -80 -60 -40 -20
Latitude (degrees)
100 -60
Longitude (degrees)
Fig. 8. Facet diameter along the dorso-ventral meridian (longitude 0 °; A) and along the equator (latitude 0 °; B). Facet diameters were
measured at each of the three possible orientations (inset in A), with curves for each represented by circles, squares and triangles respectively.
Facets are largest and most regularly hexagonal at the equator and front of the eye. D, dorsal; V, ventral; A, anterior; P, posterior.
Physiological optics in the hummingbird hawkmoth
Area (mm2)
Number of facets
Fig. 9. The area
of the
superposition aperture (eye glow), and
the number of facets comprising it, in
different parts of the eye. Both the area
and the facet number increase in a
smooth gradient towards the ventral
front of the eye and decrease in smooth
gradients dorsally and ventrally. D,
dorsal; V, ventral; A, anterior; L, lateral.
0.0 0
In a classical Exnerian superposition eye, the size and shape
of the eye glow remain constant in different parts of the eye.
Again, M. stellatarum breaks this classical rule: both the size
and shape of the eye glow vary significantly (Fig. 9) and in a
way that shows parallels to the facet variations. The eye glow
becomes largest and roundest in the anterior part of the eye,
with regard to both its area and the number of facets which
constitute it. Its largest size (350 facets, 0.25 mm2) occurs
approximately 10 ° below the equator at longitudes between
70 ° and 80 °. This region of the eye is used by M. stellatarum
for fixating the entrance of the flower during hovering. Away
from this region, the eye glow becomes smaller, decreasing in
size in smooth gradients (Fig. 9). The eye glow becomes
smallest and somewhat elliptical towards the edges of the eye.
Over large regions of the lateral eye, the eye glow maintains
approximately the same circular shape and an area of between
0.14 and 0.16 mm2. Interestingly, the eye glow area increases
slightly towards the back of the eye.
Rhabdom packing in the retina
Using the ophthalmoscope, it is possible to scan a narrow
slit across the retina and accumulate a bright image of rhabdom
rows using an image intensifier. The angle between these rows
in each orientation was measured from video prints calibrated
for angle. Such images show that the angular separation of
rhabdom rows varies considerably in different parts of the eye.
For instance, at different locations along the equator, there are
rhabdom rows oriented dorso-ventrally, and the angular
separation between these rows ∆φ decreases towards the front
of the eye (Fig. 10). At an equatorial longitude of 20 °, the rows
are 1.73 ° apart (Fig. 10A), but at a longitude of 70 ° they are
only 1.17 ° apart (Fig. 10C). Similar reductions in the angular
separations of rhabdom rows in the other two row directions
are also seen towards the front of the eye (see Fig. 11).
To quantify these changes, measurements of row separations
were made at 10 ° intervals along the posterior–anterior equator
(latitude 0 ° line) and along different dorso-ventral meridians,
in two moths (Fig. 11). At each angular position, the animal
was rotated under the ophthalmoscope in order to pick out rows
in each of the three rhabdom row orientations. We then
measured the separation of rows in the three orientations (inset,
Fig. 11A). Large variations in row separation were found in
both moths. Along meridians running dorso-ventrally
(longitude lines 15 ° in Fig. 11A and 0 ° in Fig. 11B), the
separation of dorso-ventral rows (squares in Fig. 11) remains
roughly constant. In contrast, the separation of rows in the
other two orientations (triangles and circles in Fig. 11) reaches
a minimum at the equator and increases in both the dorsal and
ventral directions. For instance, along the 0 ° longitude line
(Fig. 11B), the dorso-ventral rows remain separated by
Fig. 10. Images of dorso-ventral
rhabdom rows at three different
equatorial locations: longitudes 20 °
(A), 45 ° (B) and 70 ° (C). The images
were made by scanning a narrow slit of
light across the retina parallel to the
desired rhabdom row orientation.
During scanning, the image was
accumulated by the image intensifier
and analysis apparatus (see Fig. 2).
The angular separation of rows (∆φ)
decreases in a smooth gradient towards the front of the eye. ∆φ is 1.73 ° in A, 1.44 ° in B and 1.17 ° in C. Scale bar (for all parts), 2 °.
Animal 1
Animal 2
-60 -40 -20
20 40 60
Latitude (degrees)
20 40 60
-60 -40 -20
Latitude (degrees)
Inter-row angle (degrees)
Fig. 11. The angles separating
along two different dorsoventral meridians (longitudes
15 ° in A and 0 ° in B) and
along the anterior–posterior
equator (latitude 0 °; C,D). The
rhabdom matrix contains rows
in three different orientations,
and the angles separating rows
in each of these orientations
are shown by squares, circles
and triangles respectively
(inset in A). The angular
packing of rhabdoms is not
constant within the eye but
instead forms local acute
zones, one at the front of the
eye and another along the
equator, the equatorial one
becoming weaker posteriorly.
D, dorsal; V, ventral; A,
anterior; P, posterior.
Inter-row angle (degrees)
Longitude (degrees)
approximately 1.9 °, whereas rows in the other two orientations
reach a minimum separation of 1.3–1.4 ° at the equator,
increasing to well over 2 ° dorsally. The separations of rows in
these latter two orientations appears to be greater and to occur
more rapidly in the dorsal direction than in the ventral
direction. Measurements along the equator (Fig. 11C,D) reveal
that, even though the dorso-ventral rows are usually separated
by a much larger angle than rows in the other two orientations,
the separation of all rows decreases towards the front of the
eye. Frontally, the separations of rows in all three orientations
become very similar (approximately 1.1–1.2 °), indicating that
the angular packing of rhabdoms becomes regularly hexagonal
in this part of the eye.
The angular packing of rhabdoms in the eye indicates the
presence of retinal ‘acute zones’, a feature that is not reflected
in the packing of facets in the overlying cornea (see below).
Acute zones are regions of the eye where spatial resolution is
improved (and also quite often sensitivity) and are a wellknown adaptation in apposition eyes (Land, 1989). In M.
stellatarum, there is an acute zone along the equator of the eye
Longitude (degrees)
because the rhabdoms are mostly densely packed here
(Fig. 11A,B). This equatorial acute zone becomes even more
intense anteriorly, the region of the eye possessing the densest
packing of rhabdoms.
When we use an ophthalmoscope to look at the retina, we
do not see rhabdoms in their true physical arrangement (i.e.
with their physical separations in micrometres). Instead, we see
the rhabdoms projected in angular space, and their angular
packing may bear little resemblance to their physical packing.
The angular separation of rhabdoms ∆φ (degrees) is related to
their physical separation d (µm) via the local focal length f
(µm): ∆φ=180d/πf. If changes in ∆φ from one part of the retina
to the other are accompanied by appropriate changes in f, d
could remain constant. If this were so, then one would not
expect to see significant differences in the physical spacing of
rhabdoms within the eye. Conversely, changes in ∆φ could also
be obtained by changes in d at a fixed f, in which case the
physical spacing of rhabdoms would vary significantly within
the eye. To determine whether the changes in angular packing
we have observed can be explained by changes in f or d or
Physiological optics in the hummingbird hawkmoth
both, we made electron microscope sections from two
equatorial locations within the same eye: laterally (at longitude
0 °) and frontally (at longitude 70 °). These sections show that
the physical packing of rhabdoms is indeed denser frontally
than laterally (Fig. 12 and see Fig. 14E,F), but not dense
enough to explain the observed differences in angular packing.
This means that simultaneous changes in both d and f are
Fig. 12. Transverse electron microscope sections through the retina
at two different equatorial locations, approximately at longitudes 70 °
(A) and 0 ° (B), in the same moth. The physical rhabdom packing is
denser frontally (A) than laterally (B). Sections show the rings of
tracheal tubes which surround each rhabdom and act as a reflective
sheath for trapping light (Land, 1984a; Warrant and McIntyre, 1991).
The section in B is slightly more distal than the section in A and is,
unfortunately, not exactly perpendicular to the rhabdom axis (which
slightly exaggerates the more dilute packing present here).
Calculations based on this section (see text) have been corrected for
this. Scale bar (for both parts), 5 µm.
responsible for the changes in angular packing we have
Estimations of focal length
Knowledge of the angular (∆φ) and physical (d)
separations of rhabdom rows (Fig. 11 and see Fig. 14E,F)
allows us to calculate the focal length (f) at the lateral and
frontal equator of the eye. At both locations in the eye, the
calculated focal length is different for each of the three
different rhabdom row orientations. In the lateral eye,
f=319 µm for the dorso-ventral orientation and 350 µm and
380 µm for the other two orientations. An ‘average’ focal
length for these three values is 350 µm. In the frontal eye, the
three focal lengths are 387 µm, 424 µm and 417 µm, with an
average of 409 µm. Thus, not only do the focal lengths differ
in different parts of the eye (being longer towards the front),
they also differ between different rhabdom orientations at any
single location in the eye.
In all optical systems, including eyes, the focal length is
defined as the distance between the system’s optical ‘nodal
point’ and its focal plane. In a classical superposition eye,
there is a single nodal point located at the eye’s centre of
curvature, and the focal plane is located at the distal tips of
the rhabdoms. Because classical superposition eyes are also
spherical, the distal tips of the rhabdoms lie on a spherical
surface whose centre of curvature is the nodal point. This
means that the focal length is the same in all parts of the eye.
The fact that the focal length of the eye of M. stellatarum is
so variable suggests that the position of the nodal point may
vary with retinal location. The fact that the focal length
differs with orientation even at single retinal locations
confirms this suggestion.
Facet packing in the cornea
The angles between neighbouring facet rows in the cornea
were determined from angular displacements of the eye glow
measured using a goniometer. Angles between facet rows were
measured at 10 ° intervals along the posterior–anterior equator
(latitude 0 ° line) and along the dorso-ventral meridian
(longitude 0 ° line). At each angular position, we measured the
angular divergence of rows in each of the three facet row
orientations (inset, Fig. 13A). As with rhabdom rows, one of
the facet rows has a dorso-ventral orientation (squares,
Fig. 13).
For a large range of latitudes above and below the equator,
the angles between facet rows in all three orientations have
values of approximately 1.8–2.0 ° (Fig. 13A). For latitudes
more dorsal than 60 ° and more ventral than −50 °, the angle
between rows in all orientations increases markedly, with
angles between some rows reaching nearly 3.0 °. Along the
equator (Fig. 13B), the angles between facet rows remain
similar for all three orientations, but decline steadily towards
the front of the eye until a longitude of approximately 60 °. For
longitudes more anterior than 60 °, the angle separating dorsoventral rows suddenly increases dramatically, reaching a value
of nearly 3 ° at 90 ° longitude.
Angle between facet rows (degrees)
-80 -60 -40 -20
Longitude (degrees)
Latitude (degrees)
Fig. 13. The angles separating facet rows along the dorso-ventral meridian (longitude 0 °; A) and along the posterior–anterior equator (latitude
0 °; B). As with rhabdom rows, there are also three different orientations of facet rows, with the angular separation between rows from each
orientation shown by squares, circles and triangles respectively (inset in A). The angle separating facets is not constant in the eye, but varies in
smooth gradients. D, dorsal; V, ventral, A, anterior; P, posterior.
The number of rhabdoms per facet
To some degree the angles between the facet rows do reflect
the angles between the rhabdom rows lying directly beneath.
The facet row angles, like the rhabdom row angles, are small
near the equator (Fig. 13A) and generally decline along the
equator towards the front of the eye (Fig. 13B). However, an
inspection of Figs 11 and 13 quickly reveals that, even though
this loose relationship does exist, the angles between facets are
much larger in all parts of the eye than the angle between
rhabdoms. This can be readily seen in a comparison of the
angular packing matrices of rhabdoms and facets at two
equatorial locations on the eye (Fig. 14): laterally (at longitude
0 °) and frontally (at longitude 70 °).
The angular packing of facets at the frontal equator
(Fig. 14B) is slightly denser than at the lateral equator
(Fig. 14A), as we have already seen in Fig. 13. The same trend
is also seen in the angular packing of rhabdoms, but the density
is very much greater (and the packing more regularly
hexagonal) at the frontal equator (Fig. 14D) than at the lateral
equator (Fig. 14C). Most important, though, is the fact that the
rhabdoms are much more densely packed in both parts of the
eye than are the facets that lie above them. If this is the case
in all parts of the eye, then this means that there must be many
more rhabdoms than facets. Is this actually the case? To answer
this question, we used the data shown in Figs 11 and 13 to
calculate the local densities of rhabdoms and facets, and
Fig. 14. The physical and angular packing of rhabdoms and facets in
the eye at two different equatorial locations, laterally (longitude 0 °;
A,C,E) and frontally (longitude 70 °; B,D,F). The small circles
represent the centres of rhabdoms and facets. Both the angular (C,D)
and physical (E,F) packing of rhabdoms is denser at the front of the
eye than at the side, but the relative change is greater for angular
packing. The angular packing of facets (A,B) remains rather similar,
but much less dense, than the packing of the underlying rhabdoms.
Equatorial, lateral
Equatorial, frontal
Facet packing (angular)
Facet packing (angular)
Rhabdom packing (angular)
Rhabdom packing (angular)
Rhabdom packing (physical)
Rhabdom packing (physical)
10 µm
10 µm
Physiological optics in the hummingbird hawkmoth
Number of rhabdoms per facet
Fig. 15. The number of
rhabdoms per facet along
the dorso-ventral meridian
(longitude 0 °; A) and along
the posterior–anterior equator
(latitude 0 °; B). Except for
the extreme dorsal (and
possibly the extreme ventral)
part of the eye, the number of
rhabdoms always exceeds the
number of facets. Based on
data from two different
animals. Data points are the
averages of 3 calculations
made at each retinal location;
error bars represent their total
spread. D, dorsal; V, ventral;
A, anterior; P, posterior.
Latitude (degrees)
thereby the number of rhabdoms per facet, at 10 ° intervals
along the posterior–anterior equator (latitude 0 ° line) and
along the dorso-ventral meridian (longitude 0 ° line).
At all positions we tested along the equator, there are at least
two rhabdoms per facet, increasing to possibly as many as four
rhabdoms per facet in the extreme anterior part of the eye
(Fig. 15B). Along the dorso-ventral meridian, the number of
rhabdoms per facet is greatest near the equator (two rhabdoms
per facet) and falls systematically both dorsally and ventrally
(Fig. 15A). In the extreme dorsal part of the eye (and possibly
also in the extreme ventral part), the number of rhabdoms per
facet falls to one. As far as we can tell, these are the only places
in the eye where the number of rhabdoms and facets become
equal. Spot checks in several other parts of the eye always
revealed at least one rhabdom per facet, with most checks
revealing much higher ratios. The only conclusion that one can
draw from these results is that the eyes of M. stellatarum
possess many more rhabdoms than facets, a most remarkable
situation. In a classical superposition eye, and indeed in all
compound eyes, there should be one rhabdom per facet in all
parts of the eye. After all, an ommatidium is supposed to
contain one facet lens and one rhabdom. The fact that this is
clearly not the case in M. stellatarum is yet another indication
of how significantly this eye departs from classical Exnerian
Deviations from classical superposition design
The refracting superposition eye of the hummingbird
hawkmoth is, in many ways, the most remarkable
superposition eye ever described. Its deviation from the
principles of classical Exnerian superposition optics is so
profound that at first glance it is hard to imagine how the eye
can form a decent image at all. Yet it does, and with arguably
the sharpest receptive fields yet recorded from a superposition
eye, with acceptance angles as small as 1.3 ° in the frontal eye
(E. Warrant, K. Bartsch and C. Günther, in preparation). There
Longitude (degrees)
is no question that the departure of M. stellatarum from
classical superposition optics has given it an eye of outstanding
The eye is very non-spherical and has a retina with
rhabdoms whose packing density varies throughout the eye.
The size of the facets, the area of the superposition aperture
and the focal length also vary markedly. All these properties
are at extreme odds with the classical model of Exner (1891).
In this model, superposition eyes are spherical and maintain a
constant focal length and angular magnification throughout the
eye (i.e. the eye has a single nodal point). One would also
expect an Exnerian superposition eye to have rhabdoms of
equal length and separation and to have facets of equal size.
The variable focal length is of particular interest, because it
adds an extra degree of freedom in the design of the eye. A
single glass lens which is not circularly symmetrical, but
elongated, will often be astigmatic: the focal length in one
orientation (say X) will be different from that in the
perpendicular orientation (say Y). Because the nodal point in a
glass lens is the same for all orientations, the image planes in
the X and Y orientations will not coincide and the image quality
will be poor. Astigmatism is not a problem for M. stellatarum.
Because the nodal point can differ for different orientations at
a single retinal location, differences in focal length that occur
at that location need not mean that the image planes lack
coincidence. On the contrary, the image planes coincide
exactly on the retinal surface. Moreover, differences in focal
length mean that the image can be differently magnified in
different orientations (magnification is proportional to 1/f).
This extra degree of design freedom would permit
improvements in local spatial resolution simply by having a
magnified image (in one or more orientations). To take
advantage of this magnification, the underlying rhabdoms may
even be packed more densely.
Variations in the size of the superposition aperture have also
been noted in another diurnal moth, the agaristid Phalaenoides
tristifica (Horridge et al., 1977). In this moth, the aperture
gradually decreases from a maximum width of 15 facets in the
centre of the eye to much smaller values near the edge. In the
dorsal part of the eye, the aperture diameter falls to
approximately four facets. The eye of P. tristifica is much more
spherical than that of M. stellatarum, and it is not known
whether it possesses retinal acute zones.
The superposition eyes of M. stellatarum apparently depart
from Exnerian rules to achieve a single major benefit: the
production of local acute zones. The frontal but slightly ventral
acute zone not only has a higher spatial resolution but also
collects more light from each point in space (i.e. has larger
superposition apertures). In this region of the eye, the
rhabdoms have a rhabdom separation (∆φ) of just 1.1–1.2 °
(Fig. 11C,D) compared with more than 2 ° in some other parts
of the eye, which represents an approximately fourfold
increase in packing density. In addition to this frontal acute
zone, there is also an equatorial acute zone (Fig. 11A,B), a kind
of horizontal ‘visual streak’ to borrow the vertebrate term.
In an apposition eye, increases in ∆φ are directly visible
from the appearance of the pupil and the angular packing of
facets in the cornea (Stavenga, 1979; Land, 1989). In M.
stellatarum, however, changes in ∆φ occur only within the
retina. They are not measurable from either the pupil or the
packing of facets. According to classical Exnerian principles,
acute zones should be impossible in a superposition eye. To
quote Land (1989): ‘the option of inserting small higher
resolution regions (in superposition eyes) does not seem to be
available, because the image-forming system will not work if
there are local variations. There are superposition eyes with
regions of different resolution – in euphausiid crustaceans for
example (Land et al., 1979) – but here there are really two eyes
joined together rather than a single one with an optical
gradient.’ The eyes of M. stellatarum are the first superposition
eyes known to possess pronounced resolution gradients.
Why does the hummingbird hawkmoth have acute zones?
The rhabdom packing that leads to acute zones in the
superposition eye of M. stellatarum is actually remarkably
similar to the ommatidial packing found in the apposition eyes
of several other insects. Just as with the rhabdoms of M.
stellatarum, the ommatidia of many bees, butterflies, wasps
and locusts have their densest packing at the front of the eye,
with a smooth decrease in density occurring posteriorly along
the equator, especially between the dorso-ventral ommatidial
rows (Baumgärtner, 1928; del Portillo, 1936; Autrum and
Wiedemann, 1962; Horridge, 1978; Land, 1989). And, just as
in M. stellatarum, they also possess a horizontal visual streak.
Remarkably, the same optical adaptations have evolved in two
completely different eye designs via two completely different
Equatorial gradients of spatial resolution are thought to be
an adaptation for forward flight through a textured environment
(Land, 1989). When an insect (or any animal) moves forward,
it experiences the movement of its surroundings as it passes
them, a so-called ‘flow field’ of moving features (Gibson,
1950; Wehner, 1981; Buchner, 1984). Features directly ahead
appear to be almost stationary, while features to the side of this
forward ‘pole’ appear to move with a velocity that becomes
maximal when they are located at the side of the eye, 90 ° from
the pole. If the photoreceptors have a fixed integration time ∆t
(which is not necessarily the case), the motion of flow-field
images from front to back across the eye will cause blurring.
An object moving past the side of the eye (with velocity v) will
appear as a horizontal spatial smear whose angular size (in
degrees) will be approximately v∆t. This effectively widens the
local optical acceptance angle (∆ρ) to a new value of
√[∆ρ2+(v∆t)2] (Srinivasan and Bernard, 1975; Snyder, 1977).
The extent of this widening is worse at the side of the eye
(higher v) than at the front (lower v). To maintain an optimum
sampling ratio of ∆ρ/∆φ (Snyder, 1977, 1979), the equatorial
increase in ∆ρ posteriorly should be matched by an increase in
∆φ, as indeed seems to be the case.
A very fast flying insect such as M. stellatarum can easily
experience a velocity of 100 ° s−1 at the side of the eye. In the
lateral eye, ∆ρ=1.81 ° (Fig. 6), and assuming a value of 15 ms
for ∆t, we arrive at a new widened acceptance angle of 2.35 °,
an increase of approximately 0.5 °. The separation (∆φ) of
dorso-ventral rhabdom rows in the lateral eye is approximately
1.9 ° (Fig. 11). If we assume that the ratio of these ∆ρ and ∆φ
values is the optimum for sampling (in this case
2.35 °/1.9 °≈1.2), then we can use this ratio to predict ∆ρ
frontally (say at approximately 70 °) where widening due to
motion-blurring would be minimal. We know the value of ∆φ
is approximately 1.2 ° here (Fig. 11) and, using a sampling
ratio of 1.2, leads to a ∆ρ of 1.2×1.2 °≈1.4 °. This is exactly the
same acceptance angle as we have measured
electrophysiologically in the same part of the eye (E. Warrant,
K. Bartsch and C. Günther, in preparation).
In the case of M. stellatarum, the denser packing of
rhabdoms at the front of the eye is not just a response to lower
flow-field velocities. This acute zone also serves quite another
purpose: to fixate the entrances of flowers. When M.
stellatarum hovers and sucks nectar, it uses the frontal, and
slightly ventral, part of the eye to maintain its distance to the
flower (Knoll, 1922). If the wind blows and the flower bobs
around, it is amazing just how rapidly and effortlessly M.
stellatarum can follow the movements. To a human observer,
the moth seems almost ‘glued’ to the flower entrance by its
outstretched proboscis. This stunning ability must in part be
due to the extensive binocular overlap (E. Warrant, K. Bartsch
and C. Günther, in preparation) and excellent resolution found
in the acute zone viewing the flower entrance. The ability of
M. stellatarum to follow flower-like movements and to hold its
distance has recently been the subject of excellent behavioural
studies (Pfaff and Varju, 1991; Farina et al., 1994; Kern, 1998;
Kern and Varju, 1998). Moreover, movement-sensitive cells
with frontal receptive fields have recently been identified in the
optic lobe of M. stellatarum that would be perfect inputs to
binocular circuits designed to detect the looming of a flower
blown towards the moth (Wicklein, 1994; O’Carroll et al.,
The horizontal ‘visual streak’ possessed by M. stellatarum,
and by other fast-flying insects which live in open terrain, is
Physiological optics in the hummingbird hawkmoth
possibly an adaptation for horizon detection. The horizon is a
major visual cue in natural scenes, a large contrasting border
between a blue-ultraviolet sky and a green-brown landscape.
In many insects, the ocelli play a major role in detecting this
horizon (Wilson, 1978; Stange, 1981), but in M. stellatarum,
which has no ocelli, the eyes are solely responsible. A
surprising number of visually interesting things are located at
the horizon, familiar landmarks for instance. Because of this,
visual streaks have evolved which sample the horizon much
more densely than other parts of the vertical visual field. Visual
streaks are common in vertebrates (for a review, see Hughes,
1977) and in the compound eyes of arthropods (for reviews,
see Wehner, 1987; Land, 1989). They have never before been
reported in a superposition eye. Hovering insects such as M.
stellatarum may find the horizon very useful for preventing
themselves from ‘rolling’ around their long axes during
hovering. Interestingly, cells have recently been described in
the ventral nerve cord of M. stellatarum that respond strongly
to upward and downward motion of laterally placed horizontal
edges (Kern, 1994, 1998; Kern and Varju, 1998). Moreover,
the response of these putative roll detectors is strongest when
a horizontal edge moves over the equator of the eye, a result
that fits very well with the presence of an equatorial visual
A compound eye without ommatidia
The superposition eye of the hummingbird hawkmoth is a
compound eye without functional ommatidia. An ommatidium
contains one set of rhabdomeres, which together constitute a
rhabdom, and one pair of lenses, the corneal facet lens and the
crystalline cone. In M. stellatarum, there are clearly many
more rhabdoms than facets (Figs 14, 15), and therefore the
ommatidial ratio of one rhabdom per facet has been
abandoned. Simply put, there are no ommatidia in the
functional sense, and there is no interommatidial angle.
Instead, there is a matrix of photoreceptors and an overlying
imaging system made out of a completely independent matrix
of lens elements. In a sense, this is a compound eye that has
developed into a kind of simple eye, like that in a spider: a
retina with a fovea receiving a bright sharp image from an
independent lens.
What does M. stellatarum gain by lacking true ommatidia?
First, because the rhabdoms are not constrained by an
ommatidial matrix, they are free to aggregate and to form
acute zones in a way impossible for a normal superposition
eye. Second, because the facets are not constrained by the
rhabdom matrix, they are free to vary optically and
morphologically, and this they do spectacularly. Their optical
variation has allowed them to develop a gradient of
superposition apertures, the largest of which are centred
exactly over the frontal acute zone in the retina, the region
responsible for flower fixation (Fig. 9). Not only this, the
facets here are also the largest in the eye (Fig. 8), and larger
facets are less affected by the image-degrading effects of
diffraction. The flower-fixating part of the eye produces the
brightest, sharpest image on the acutest part of the retina. This
region has the highest sensitivity and the greatest resolution
of the entire eye, and entirely due to the eye’s radical
departure from the classical superposition design.
Superposition eyes without ommatidia, whilst rare, are
not unheard of. Cases are known from the dorsal eyes of
male mayflies (Zimmer, 1898; Wolburg-Buchholz, 1976; P.
Brännström and D.-E. Nilsson, in preparation), the dorsal acute
zones of euphausiid shrimps (Chun, 1896; Land et al., 1979)
and the larval eye of the euphausiid Thysanopoda tricuspidata,
which has 90 rhabdoms but only seven facets (Land, 1981,
1984b). The most extreme example is the mysid shrimp
Dioptromysis paucispinosa, which has a superposition eye that
in all respects is quite classical apart from the presence of a
single enormous facet supplying light to its own private acute
zone of 120 rhabdoms (Nilsson and Modlin, 1994). But, as we
mentioned above, if any changes in resolution are seen in these
eyes, it is because of the presence of two separate regions, each
with uniform resolution, that have been joined together to form
a single eye. The superposition eye of M. stellatarum is the
first documented example of a superposition eye with true
gradients. Interestingly, new data from the nocturnal
hawkmoth Deilephila elphenor also show weak gradients, but
in an eye that looks quite spherical and has the same number
of rhabdoms as facets (P. Brännström and Y. Arroyo Yanguas,
in preparation).
It is not yet understood how superposition eyes can develop
with an unequal number of facets and rhabdoms. It would seem
that during the manufacture of ommatidia some must develop
without lenses.
How can M. stellatarum break all the rules and get away with
Unfortunately, the answer to this question still remains a
mystery. The fact that the focal length varies at different points
in the eye, and even at the same point, presents a major
conceptual difficulty in understanding this eye. Quite clearly,
the optical nodal point has no single location and probably has
nothing at all to do with the local curvature of the retina, as it
does in a classical superposition eye. Both the retina and the
overlying cornea are highly aspherical and are not concentric,
which means that the depth of the clear zone varies all over the
eye. The depth of the clear zone indicates the distance between
the optics and the image plane at the distal tips of the rhabdoms
(McIntyre and Caveney, 1985). The fact that it varies means
there must be a compensatory change in the optics to maintain
a crisp image on the rhabdom tips. This must somehow be
achieved by systematically altering the optics and morphology
of the lenses, something that is difficult to conceive because
the same crystalline cone can be used to focus light from two
entirely different incident angles to two entirely different
locations on the retina. How can a single crystalline cone
manage two different clear zone depths, compensating for the
difference by bending light by different amounts for the two
different locations? This would require that the angular
magnifications of individual cones are not constant (as in
Exnerian eyes), but vary with the angle of incidence of
incoming light. Interestingly, recent work suggests that this
could indeed be the case in the unusual dorsal superposition
eyes of krill and mayflies, which have highly curved corneal
surfaces and flat retinas (D.-E. Nilsson, P. Brännström and L.
Gislén, in preparation). The same problem arises when
thinking about the variable superposition aperture. A single
crystalline cone could be optically functional in two different
superposition apertures. Again it is difficult to understand how
this can work unless the optical magnifications of individual
cones can vary with the angle of incident light. Land (1989)
was not being naive by claiming that gradients are impossible
in superposition eyes. They really do seem impossible.
Obviously, however, they are not only possible, they also
produce superposition eyes of unsurpassed quality. Exactly
how is still unclear.
This study is dedicated to Professor Dezsö Varju on the
occasion of his retirement from the Chair of Biological
Cybernetics at the University of Tübingen. The authors are
extremely grateful to Dan-Eric Nilsson for critically reading the
manuscript and for many fruitful discussions. Both he, HansJürgen Dahmen and Mike Land graciously allowed us to use
their equipment and willingly assisted us with its operation.
Dezsö Varju, Hans-Jürgen Dahmen, Mike Land, Martina
Wicklein, Almut Kelber and Michael Pfaff were also a source
of rich insight. We are extremely indebted to Rita Wallén and
Lina Hansen for expert histological work. This study would
have been impossible without the gratefully acknowledged
assistance of a Twinning Grant provided by the European
Science Foundation. K.B. is grateful for support from the
Deutsche Forschungsgemeinschaft (SFB 307). E.J.W. is deeply
grateful for the ongoing support of the Swedish Natural Science
Research Council and for the generous hospitality extended to
him by Professor Varju and the other members of his Tübingen
department during many memorable visits. This paper was
completed during a Fellowship at the Institute of Advanced
Study in Berlin, for whose support and marvellous working
environment E.J.W. is particularly grateful.
Autrum, H. and Wiedemann, I. (1962). Versuche über den
Strahlengang im Insektenauge. Z. Naturforsch. 17b, 480–482.
Bartsch, K. and Warrant, E. J. (1994). The non-spherical
superposition eye of Macroglossum stellatarum (Lepidoptera,
Sphingidae). In Göttingen Neurobiology Report 1994 (ed. N. Elsner
and H. Breer), p. 434. Stuttgart, New York: Georg Thieme Verlag.
Baumgärtner, H. (1928). Der Formensinn und die Sehschärfe der
Bienen. Z. Vergl. Physiol. 7, 56–143.
Buchner, E. (1984). Behavioural analysis of spatial vision in insects.
In Photoreception and Vision in Invertebrates (ed. M. A. Ali), pp.
561–621. New York, London: Plenum.
Chun, C. (1896). Atlantis. Biologische Studien über pelagische
Organismen. Zoologica, Stuttgart 7, 1–260.
Dahmen, H. (1991). Eye specialisation in waterstriders: an adaptation
to life in a flat world. J. Comp. Physiol. A 169, 623–632.
del Portillo, J. (1936). Beziehungen zwischen den Öffnungswinkeln
der Ommatidien, Krümmung und Gestalt der Insekten-Augen und
ihrer funktionellen Aufgabe. Z. Vergl. Physiol. 23, 100–145.
Exner, S. (1891). Die Physiologie der facettirten Augen von
Krebsen und Insecten. Franz Deuticke, Leipzig Vienna. English
translation: R. C. Hardie (1988) The Physiology of the Compound
Eyes of Insects and Crustaceans. Berlin, Heidelberg, New York:
Farina, W. M., Kramer, D. and Varju, D. (1995). The response of
the hovering hawkmoth Macroglossum stellatarum to translatory
pattern motion. J. Comp. Physiol. A 176, 551–562.
Farina, W. M., Varju, D. and Zhou, Y. (1994). The regulation of
distance to dummy flowers during hovering flight in the hawkmoth
Macroglossum stellatarum. J. Comp. Physiol. A 174, 239–247.
Gibson, J. J. (1950). The Perception of the Visual World. Boston:
Houghton Mifflin Company.
Horridge, G. A. (1978). The separation of visual axes in apposition
compound eyes. Phil. Trans. R. Soc. Lond. B 285, 1–59.
Horridge, G. A., McLean, M., Stange, G. and Lillywhite, P. G.
(1977). A diurnal moth superposition eye with high resolution
Phalaenoides tristifica (Agaristidae). Proc. R. Soc. Lond. B 196,
Hughes, A. (1977). The topography of vision in mammals of
contrasting life style: comparative optics and retinal organisation.
In Handbook of Sensory Physiology, vol. VII/5 (ed. F. Crescitelli),
pp. 613–756. Berlin, Heidelberg, New York: Springer.
Kelber, A. (1996). Colour learning in the hawkmoth Macroglossum
stellatarum. J. Exp. Biol. 199, 1127–1131.
Kelber, A. (1997). Innate preferences for flower features in
the hawkmoth Macroglossum stellatarum. J. Exp. Biol. 200,
Kelber, A. and Pfaff, M. (1997). Spontaneous and learned
preferences for visual flower features in a diurnal hawkmoth. Israel.
J. Plant Sci. 45, 235–245.
Kelber, A. and Henique, U. (1999). Trichromatic colour vision in
the hummingbird hawkmoth Macroglossum stellatarum L. J.
Comp. Physiol. A (in press).
Kern, R. (1994). Mechanisms underlying visual position stabilization
in the hovering hawk moth Macroglossum stellatarum L. Doctoral
dissertation, University of Tübingen, Germany.
Kern, R. (1998). Visual position stabilization in the hummingbird
hawk moth, Macroglossum stellatarum L. II. Electrophysiological
analysis of neurons sensitive to wide-field image motion. J. Comp.
Physiol. A 182, 239–249.
Kern, R. and Varju, D. (1994). Flow-field analysis by means of eye
region specialisation: free flight experiments in the hawkmoth
Macroglossum. In Proceedings of the 22nd Göttingen
Neurobiology Conference (ed. N. Elsner and H. Breer), p. 435.
Stuttgart, New York: Georg Thieme Verlag.
Kern, R. and Varju, D. (1998). Visual position stabilization in the
hummingbird hawk moth, Macroglossum stellatarum L. I.
Behavioural analysis. J. Comp. Physiol. A 182, 225–237.
Knoll, F. (1922). Lichtsinn und Blumenbesuch des Falters von
Macroglossum stellatarum. Abh. Zool. Botan. Ges. Wien 12,
Land, M. F. (1981). Optics and vision in invertebrates. In Handbook
of Sensory Physiology, vol. VII/6B (ed. H. Autrum), pp. 471–592.
Berlin, Heidelberg, New York: Springer.
Land, M. F. (1984a). The resolving power of diurnal superposition
eyes measured with an ophthalmoscope. J. Comp. Physiol. 154,
Land, M. F. (1984b). Crustacea. In Photoreception and Vision in
Physiological optics in the hummingbird hawkmoth
Invertebrates (ed. M. A. Ali), pp. 401–438. New York, London:
Land, M. F. (1989). Variations in the structure and design of
compound eyes. In Facets of Vision (ed. D. G. Stavenga and R. C.
Hardie), pp. 90–111. Berlin, Heidelberg, New York, London, Paris,
Tokyo: Springer.
Land, M. F., Burton, F. A. and Meyer-Rochow, V. B. (1979). The
optical geometry of euphausiid eyes. J. Comp. Physiol. 130, 49–62.
McIntyre, P. D. and Caveney, S. (1985). Graded-index optics are
matched to optical geometry in the superposition eyes of scarab
beetles. Phil. Trans. R. Soc. Lond. B 311, 237–269.
Nilsson, D.-E. and Modlin, R. F. (1994). A mysid shrimp carrying
a pair of binoculars. J. Exp. Biol. 189, 213–236.
O’Carroll, D., Bidwell, N. J., Laughlin, S. B. and Harris, R. A.
(1997). Spatio-temporal properties of motion detectors matched to
low image velocities in hovering insects. Vision Res. 37,
Pfaff, M. and Varju, D. (1991). Mechanisms of visual distance
perception in the hawk moth Macroglossum stellatarum. Zool. Jb.
Physiol. 95, 315–321.
Snyder, A. W. (1977). Acuity of compound eyes: physical limitations
and design. J. Comp. Physiol. 116, 161–182.
Snyder, A. W. (1979). Physics of vision in compound eyes. In
Handbook of Sensory Physiology, vol. VII/6A (ed. H. Autrum), pp.
225–313. Berlin, Heidelberg, New York: Springer.
Srinivasan, M. V. and Bernard, G. D. (1975). The effect of motion
on visual acuity of the compound eye: a theoretical analysis. Vision
Res. 15, 515–525.
Stange, G. (1981). The ocellar component of flight equilibrium
control in dragonflies. J. Comp. Physiol. 141, 335–347.
Stavenga, D. G. (1979). Pseudopupils of compound eyes. In
Handbook of Sensory Physiology, vol. VII/6A (ed. H. Autrum), pp.
357–439. Berlin, Heidelberg, New York: Springer.
Warrant, E. J. and McIntyre, P. D. (1991). Strategies for retinal
design in arthropod eyes of low F-number. J. Comp. Physiol. A
168, 499–512.
Warrant, E. J. and McIntyre, P. D. (1996). The visual ecology of
pupillary action in superposition eyes. J. Comp. Physiol. A 178,
Wehner, R. (1981). Spatial vision in arthropods. In Handbook of
Sensory Physiology, vol. VII/6C (ed. H. Autrum), pp. 287–616.
Berlin, Heidelberg, New York: Springer.
Wehner, R. (1987). ‘Matched filters’ – neural models of the external
world. J. Comp. Physiol. A 161, 511–531.
Wicklein, M. (1994). Neuroanatomie der optischen Ganglien und
Elektrophysiologie bewegungssensitiver Interneurone in der
Lobula Platte des Taubenschwanzes Macroglossum stellatarum
(Sphingidae, Lepidoptera). Doctoral dissertation, University of
Tübingen, Germany.
Wilson, M. (1978). The functional organisation of locust ocelli. J.
Comp. Physiol. 124, 297–316.
Wolburg-Buchholz, K. (1976). The dorsal eye of Cloeon dipterum
(Ephemeroptera). A light and electron microscopical study. Z.
Naturforsch. 31c, 335–336.
Zimmer, C. (1898). Die Facettenaugen der Ephemeriden. Z. Wiss.
Zool. 63, 236–261.