Limb darkening in this image of today’s Sun

I was given a proper solar filter for my birthday about 1,5 month ago and I hadn’t taken a single photograph through it. Until today. Today, around noon, I took this (pretty awesome) picture of the Sun:

40 frame stack of the Sun at 12.00 GMT+1, as seen from Enschede

40 frame stack of the Sun at the 21st of nov. 2014, 12.00 GMT+1, as seen from Enschede

In this image (which I colored yellow-orange-ish because you probably feel more familiar with a yellow sun than a white one), the outer regions of the Sun appear clearly less bright than near the center. This is a well studied effect and is called ‘limb darkening’. In the Eddington approximation, the intensity depends on the angle between the outgoing light and the axis perpendicular to the surface. The equation that describes this intensity is not more difficult than one cosine and 2 fractions:

limb_darkening

In the figure below, I have added 3 blue bars on the Sun’s disk, with their corresponding angles. The intensities given by measuring the mean pixel values that my DSLR gives me, are probably not the most accurate, but they are the best I can do (the intensity gradient is probably altered by the used solar filter and the DSLR settings). I have normalized the mean values with the maximum pixel value of 255 so that my measured values become 0.72 in the center, 0.60 at 71% of the radius and 0.28 at the edge of the Sun.

Measured intensities at different angles

Measured intensities at different angles

In the table below I have listed the measured values and those given by the equation I showed you. The fact that the value for theta=0 is the same was to be expected since I used this as the center intensity. The fact that the other 2 values correspond very good however, comes as quite a surprise. I didn’t really expect it to be this accurate, but the changes in contrast caused by the equipment and software seem to balance out pretty good.

table of measured and calculated values

Anyway, I just wanted to show you that the predicted limb darkening is apparent in the photo I made 🙂

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My newest toy: A microscope!

After my postponed birthday party this weekend, I was one microscope richer. A friend of mine hadn’t used his microscope for a while and decided it would be a kick-ass birthday gift. Well he’s right…. it is!

Firstly, I cut off the tiniest bit of a Brassia orchid leaf and stuck it between a glass slide and cover. I found it hard to keep my eye at a steady distance, so I fitted a rubber eye shield which I had left from an old telescope eyepiece. This also improved sight, because it shields light from outside obviously.

I think you can guess what I fitted to the microscope next…. yep: my camera! My telescope adapter fits almost perfectly.

As the depth of focus of the microscope is not very deep, I have to make multiple photos with different heights of the object in focus and stack them. For this I used photoshop and I was quite surprised with the result.

Leaf of a Brassia orchid. This is a stack of photos taken with different regions in focus.

Leaf of a Brassia orchid. This is a stack of photos taken with different regions in focus.

I heard that liquor also looks awesome through a microscope, so I took a droplet of absinthe. As might have been expected, nothing special, just transparency. Some crystallized absinthe (mostly sugar) that I scraped off the bottle gave better results, although I think there definitely are alcoholic beverages that look even better.

Crystallized absinthe, scraped from the bottle opening. B/W stack

Crystallized absinthe, scraped from the bottle opening. B/W stack

While searching the house for other food and beverages that may look awesome when magnified, I decided to have a coffee and came across some roasted, ground coffee beans of which I sprinkled some on a glass slide. Making photos at all different focal depths was quite a hastle, but it sure was worth it. Here’s what you use to make your morning coffee 😛

Microscopic photo of roasted ground coffee beans for making filter coffee.

Microscopic photo of roasted ground coffee beans for making filter coffee.

When I was busy putting chalk between glass, I didn’t think about the fact that it will stick to both the glass slide and the cover glass. So it turned out different from what I expected.

Stacked photos of chalk sticking to the glass slide and the cover glass.

Stacked photos of chalk sticking to the glass slide and the cover glass.

You may have noticed that further away from the center of the photos, the blue and red channels are somewhat misaligned. I will try to use single channels to get rid of this and get sharper images, albeit in black and white.

I sure had fun while toying around with the microscope and camera and it probably wont be long until I post my next photos 😉

Then I would like to share another evening sky photo with you. Moist air isn’t very astronomer-friendly, but there’s no denying that it makes some lovely evening pictures.

Another nice evening sky

Another nice evening sky

While typing this, I have my telescope up and running outside and am waiting for the Horsehead and Flame nebula to rise a little further above the horizon. There currently are faint clouds in front of it. I already shot some cool photos of the Dumbbell Nebula which I will probably post tomorrow 🙂