wp_dropdown_pages as an option in my widget

nI’ve created a widget for users to choose an image to display in the side bar that links to a page of their choice. I’d like that page to be selected via wp_dropdown_pages.

I am good on the part of having users set the image url, height and width, but saving the target is where I’m stuck.

class detc_cta_widget extends WP_Widget {

// Constructor //

function detc_cta_widget() {
    $widget_ops = array( 'classname' => 'detc_cta_widget', 'description' => 'Displays a Phone CTA' ); // Widget Settings
    $control_ops = array( 'id_base' => 'detc_cta_widget' ); // Widget Control Settings
    $this->WP_Widget( 'detc_cta_widget', 'DETC - CTA', $widget_ops, $control_ops ); // Create the widget
}

// Extract Args //

    function widget($args, $instance) {
        extract( $args );
        $title  = apply_filters('widget_title', $instance['title']); // the widget title
        $img_source     = $instance['img_source']; // CTA Image Source URL
        $img_height     = $instance['img_height']; // CTA Image Height
        $img_width  = $instance['img_width']; // CTA Image Width
        $link_target    = $instance['link_target']; // CTA Link Target

// Before widget //

        echo $before_widget;

// Title of widget //

        if ( $title ) { echo $before_title . $title . $after_title; }

// Widget output //
        ?>
        <div>
        <a href="<?php echo $link_target ?>"><img src="<?php echo $img_source ?>" height="<?php echo $img_height ?>" width="<?php echo $img_width ?>"></a>
        </div>
        <?php

// After widget //

        echo $after_widget;

    }

// Update Settings //

    function update($new_instance, $old_instance) {
        $instance['title'] = strip_tags($new_instance['title']);
        $instance['img_source'] = strip_tags($new_instance['img_source']);
        $instance['img_height'] = strip_tags($new_instance['img_height']);
        $instance['img_width'] = strip_tags($new_instance['img_width']);
        $instance['link_target'] = strip_tags($new_instance['link_target']);
        return $instance;
    }

// Widget Control Panel //

    function form($instance) {

    $defaults = array( 'title' => '','img_source' => 'wp-content/themes/corvius/images/cta_img.png','img_height' => '50','img_width' => '200','link_target' => 'cta.php');
    $instance = wp_parse_args( (array) $instance, $defaults ); ?>

    <p>
        <label for="<?php echo $this->get_field_id('title'); ?>">Title:</label>
        <input class="widefat" id="<?php echo $this->get_field_id('title'); ?>" name="<?php echo $this->get_field_name('title'); ?>'" type="text" value="<?php echo $instance['title']; ?>" />
    </p>
    <p>
        <label for="<?php echo $this->get_field_id('img_source'); ?>"><?php _e('CTA Image URL:'); ?></label>
        <input class="widefat" id="<?php echo $this->get_field_id('img_source'); ?>" name="<?php echo $this->get_field_name('img_source'); ?>" type="text" value="<?php echo $instance['img_source']; ?>" />
    </p>
    <p>
        <label for="<?php echo $this->get_field_id('img_height'); ?>"><?php _e('CTA Image Height:'); ?></label>
        <input class="widefat" id="<?php echo $this->get_field_id('img_height'); ?>" name="<?php echo $this->get_field_name('img_height'); ?>" type="text" value="<?php echo $instance['img_height']; ?>" />
    </p>
    <p>
        <label for="<?php echo $this->get_field_id('img_width'); ?>"><?php _e('CTA Image Width:'); ?></label>
        <input class="widefat" id="<?php echo $this->get_field_id('img_width'); ?>" name="<?php echo $this->get_field_name('img_width'); ?>" type="text" value="<?php echo $instance['img_width']; ?>" />
    </p>
    <p>
        <label for="<?php echo $this->get_field_id('link_target'); ?>"><?php _e('CTA Link Target:'); ?></label>
        <?php wp_dropdown_pages(); ?>
    </p>



    <?php }


}
// End class detc_cta_widget

add_action('widgets_init', create_function('', 'return register_widget("detc_cta_widget");'));
?>

This is what the Widget Options Area looks like:

UPDATE:
@Simon
I’ve changed the Control Panel code to:

    <p>
        <label for="<?php echo $this->get_field_id('link_target'); ?>"><?php _e('CTA Link Target:'); ?></label>
        <?php wp_dropdown_pages(array('id' => $this->get_field_id('link_target'),'name' => $this->get_field_name('link_target'))); ?>
    </p>

But still no success in the selection being saved.