  A major science goal of future, large-aperture, optical space telescopes is
to directly image and spectroscopically analyze reflected light from
potentially habitable exoplanets. To accomplish this, the optical system must
suppress diffracted light from the star to reveal point sources approximately
ten orders of magnitude fainter than the host star at small angular separation.
Coronagraphs with microdot apodizers achieve the theoretical performance needed
to image Earth-like planets with a range of possible telescope designs,
including those with obscured and segmented pupils. A test microdot apodizer
with various bulk patterns (step functions, gradients, and sinusoids) and 4
different dot sizes (3, 5, 7, and 10 $\mu$m) made of small chrome squares on
anti-reflective glass was characterized with microscopy, optical laser
interferometry, as well as transmission and reflectance measurements at
wavelengths of 600 and 800 nm. Microscopy revealed the microdots were
fabricated to high precision. Results from laser interferometry showed that the
phase shifts observed in reflection vary with the local microdot fill factor.
Transmission measurements showed that microdot fill factor and transmission
were linearly related for dot sizes >5 $\mu$m. However, anomalously high
transmittance was measured when the dot size is <5x the wavelength and the fill
factor is approximately 50%, where the microdot pattern becomes periodic. The
transmission excess is not as prominent in the case of larger dot sizes
suggesting that it is likely to be caused by the interaction between the
incident field and electronic resonances in the surface of the metallic
microdots. We used our empirical models of the microdot apodizers to optimize a
second generation of reflective apodizer designs and confirmed that the
amplitude and phase of the reflected beam closely matches the ideal wavefront.
