How to make thumbnails using Imagick::resizeImage appear sharper - PHP?

I am using Imagick::resizeImage to create a thumbnail PNG image of each page of a pdf file. However, the image I am getting back is really blurry. How can I make it a little sharper? Any pointers would be really appreciated.

I have tried adjusting the 'blur' paramter of Imagick::resizeImage between 0.1 - 1, without success.

$pdfPage = '1Mpublic.pdf[0]';
$im = new imagick($pdfPage);
$im->setImageFormat('png');

// Resize thumbnail image
$imgHeight =  $im -> getImageHeight();
$imgWidth = $im -> getImageWidth();
$desiredWidth = 200;
$desiredHeight = resizedImageHeight($imgWidth, $imgHeight, $desiredWidth);

$im -> setResolution(1500, 1500);
$im -> resizeImage($desiredWidth, $desiredHeight, imagick::STYLE_NORMAL, 0.1);

 /* Resize image */
function resizedImageHeight($imgWidth, $imgHeight, $desiredImgWidth){

    $quoient = $imgWidth/$imgHeight;
    $height = $desiredImgWidth/$quoient;

    return $height;
}

original pdf link:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4905263/pdf/ksgt-06-04-1091539.pdf

Rather than rendering and then resizing the raster, it might be better to render the PDF to the right number of pixels in the first place. It'll be faster, and you can be sure that the amount of sharpness is correct for the content.

For example:

$ time convert -density 50 ksgt-06-04-1091539.pdf[0] x2.png
real    0m0.325s
user    0m0.299s
sys 0m0.024s

Makes:

The -density 50 makes a page about the same number of pixels across as your sample, 425.

In imagick you could do it like this (as @fmw42's excellent answer already says):

#!/usr/bin/env php
<?php

$target_width = 400;

# get natural size, calculate density we need for target width
$im = new imagick();
$im->pingImage($argv[1]);
$geo = $im->getImageGeometry();
$natural_width = $geo['width'];
$density = 72.0 * $target_width / $natural_width;

# load at correct resolution for target_width
$im = new imagick();
$im->setResolution($density, $density);
$im->readImage($argv[1]);

# and write back
$im->writeImage($argv[2]);

Doing both the ping and the read is a little slow in imagick, unfortunately:

$ time ./pdfthumb.php ksgt-06-04-1091539.pdf x.png
real    0m2.773s
user    0m2.737s
sys 0m0.036s

It's not imagick, but vipsthumbnail can do the ping and read in one operation:

$ time vipsthumbnail ksgt-06-04-1091539.pdf -s 400x -o x2.png
real    0m0.064s
user    0m0.064s
sys 0m0.011s

It might be worth considering if speed is important. libvips has a php binding so you can call it directly, but if you do that you'll run into awful licensing problems because it uses the GPL library poppler for PDF rendering, sigh. ImageMagick uses GhostScript and shells out to that for the same reason.