i haven’t used the refractometer you are using but i have home experience with the atago and work experience with the vst, so i will try to help you out.
the only espresso filters i am aware of are vst espresso filters. they are about a dollar a pop, and probably shouldn’t be reused if you want to be sure of the accuracy of your sample reading. i’m sure there are other brands out there, but i know for sure that these work, and that is saying a lot after recently realizing that certain kinds of v60 filters don’t filter enough solids out to get a stable refractometer reading. it might save you time and trouble from a run-around and a headache, by just buying the vst espresso filters right from the beginning. you can find them through a coffee equipment supplier on-line, and will have to get a ten milliliter espresso syringe with them. the syringe IS reusable.
without the filter on the syringe, draw up a few mils of your espresso, not from the bottom of the cup where the most sediment is, and not from the top of the cup where the crema is, but in the middle. pump it in and out a couple of times to mix it, then leave a few mils in the syringe and screw the filter on the end of the syringe with the larger filter opening.
i usually purge the first drop or two into the trash or something. i have no reason to know that this is necessary, just seems right. the next three or so drops should be into the refractometer’s sample dish. then you activate the refractometer and it should give you a reading in a dissolved solids to water percentage. maybe 8-11%
that’s your tds! now just wipe the sample out with a soft tissue, and again with a wet tissue or cotton ball to make sure the lense is clean for your next sample. then pump some water through your syringe to clean it, and leave it pressed all the way down to remove the water.
i left out the step of cooling. your sample should cool to the approx temp of your refractometer in order to have consistent results. this takes a few minutes, and if you remove your sample to be filtered from the rest of your espresso shot, it can cool a little quicker being a smaller amount of liquid. you could filter some of the espresso into a clean demitasse to cool and then transfer it with a clean pipette, or if you wish, you can let the three filtered drops cool in the refractometer sample dish. you can take readings while it cools over the next three minutes or so, and when the reading stops changing and stabilizes, that is your truest reading.